JEE Main & Advanced Mathematics Conic Sections Question Bank

done Parabola Total Questions - 166

• question_answer1)
  If a double ordinate of the parabola \[{{y}^{2}}=4ax\] be of length \[8a\], then the angle between the lines joining the vertex of the parabola to the ends of this double ordinate is
  A)
             30o  done clear
  B)
             60o done clear
  C)
             90o  done clear
  D)
             120o done clear
  View Solution play_arrow

• question_answer2)
  PQ is a double ordinate of the parabola\[{{y}^{2}}=4ax\]. The locus of the points of trisection of PQ is
  A)
             \[9{{y}^{2}}=4ax\]                      done clear
  B)
             \[9{{x}^{2}}=4ay\] done clear
  C)
             \[9{{y}^{2}}+4ax=0\]                  done clear
  D)
             \[9{{x}^{2}}+4ay=0\] done clear
  View Solution play_arrow

• question_answer3)
  If the vertex of a parabola be at origin and directrix be \[x+5=0\], then its latus rectum is               [RPET 1991]
  A)
             5      done clear
  B)
             10 done clear
  C)
             20    done clear
  D)
             40 done clear
  View Solution play_arrow

• question_answer4)
  The latus rectum of a parabola whose directrix is \[x+y-2=0\] and focus is (3, ? 4), is
  A)
             \[-3\sqrt{2}\]                             done clear
  B)
             \[3\sqrt{2}\] done clear
  C)
             \[-3/\sqrt{2}\]                           done clear
  D)
             \[3/\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer5)
  The equation of the lines joining the vertex of the parabola \[{{y}^{2}}=6x\] to the points on it whose abscissa is 24, is
  A)
             \[y\pm 2x=0\]                            done clear
  B)
             \[2y\pm x=0\] done clear
  C)
             \[x\pm 2y=0\]                            done clear
  D)
             \[2x\pm y=0\] done clear
  View Solution play_arrow

• question_answer6)
  The points on the parabola \[{{y}^{2}}=36x\] whose ordinate is three times the abscissa are
  A)
             (0, 0), (4, 12)                              done clear
  B)
             (1, 3),(4, 12) done clear
  C)
             (4, 12)                                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer7)
  The points on the parabola \[{{y}^{2}}=12x\] whose focal distance is 4, are
  A)
             \[(2,\ \sqrt{3}),\ (2,\ -\sqrt{3})\]      done clear
  B)
             \[(1,\ 2\sqrt{3}),\ (1,-2\sqrt{3})\] done clear
  C)
             (1, 2)                                          done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer8)
  The focal distance of a point on the parabola \[{{y}^{2}}=16x\] whose ordinate is twice the abscissa, is
  A)
             6      done clear
  B)
             8 done clear
  C)
             10    done clear
  D)
             12 done clear
  View Solution play_arrow

• question_answer9)
  The co-ordinates of the extremities of the latus rectum of the parabola \[5{{y}^{2}}=4x\] are
  A)
             \[(1/5,\ 2/5),\ (-1/5,\ 2/5)\]     done clear
  B)
             \[(1/5,\ 2/5),\ (1/5,\ -2/5)\] done clear
  C)
             \[(1/5,\ 4/5),\ (1/5,\ -4/5)\]     done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer10)
  A parabola passing through the point \[(-4,\ -2)\] has its vertex at the origin and y-axis as its axis. The latus rectum of the parabola is
  A)
             6      done clear
  B)
             8 done clear
  C)
             10    done clear
  D)
             12 done clear
  View Solution play_arrow

• question_answer11)
  The focus of the parabola \[{{x}^{2}}=-16y\] is  [RPET 1987; MP PET 1988, 92]
  A)
             (4, 0)                                          done clear
  B)
             (0, 4) done clear
  C)
             (?4, 0)                                        done clear
  D)
             (0, ?4) done clear
  View Solution play_arrow

• question_answer12)
  If (2, 0) is the vertex and y-axis the directrix of a parabola, then its focus is       [MNR 1981]
  A)
             (2, 0)                                          done clear
  B)
             (­?2, 0) done clear
  C)
             (4, 0)                                          done clear
  D)
             (?4, 0) done clear
  View Solution play_arrow

• question_answer13)
  If the parabola \[{{y}^{2}}=4ax\] passes through (?3, 2), then length of its latus rectum is               [RPET 1986, 95]
  A)
             2/3 done clear
  B)
             1/3 done clear
  C)
             4/3  done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer14)
  The ends of latus rectum of parabola \[{{x}^{2}}+8y=0\] are [MP PET 1995]
  A)
             (?4, ?2) and (4, 2)                      done clear
  B)
             (4, ?2) and (?4, 2) done clear
  C)
             (?4, ?2) and (4, ?2)                    done clear
  D)
             (4, 2) and (?4, 2) done clear
  View Solution play_arrow

• question_answer15)
  The end points of latus rectum of the parabola \[{{x}^{2}}=4ay\] are [RPET 1997]
  A)
             \[(a,\ 2a),\ (2a,\ -a)\]               done clear
  B)
             \[(-a,\ 2a),\ (2a,\ a)\] done clear
  C)
             \[(a,\ -2a),\ (2a,\ a)\]               done clear
  D)
             \[(-2a,\ a),\ (2a,\ a)\] done clear
  View Solution play_arrow

• question_answer16)
  The equation of the parabola with its vertex at the origin, axis on the y-axis and passing through the point (6, ?3) is [MP PET 2001]
  A)
             \[{{y}^{2}}=12x+6\]                    done clear
  B)
             \[{{x}^{2}}=12y\] done clear
  C)
             \[{{x}^{2}}=-12y\]                      done clear
  D)
             \[{{y}^{2}}=-12x+6\] done clear
  View Solution play_arrow

• question_answer17)
  Focus and directrix of the parabola \[{{x}^{2}}=-8ay\] are [RPET 2001]
  A)
             \[(0,\ -2a)\ \text{and}\ y=2a\] done clear
  B)
             \[(0,\ 2a)\ \text{and}\ y=-2a\] done clear
  C)
             \[(2a,\ 0)\ \text{and}\ x=-2a\]  done clear
  D)
             \[(-2a,\ 0)\ \text{and}\ x=2a\] done clear
  View Solution play_arrow

• question_answer18)
  The equation of the parabola with focus (3, 0) and the directirx \[x+3=0\] is     [EAMCET 2002]
  A)
             \[{{y}^{2}}=3x\]                          done clear
  B)
             \[{{y}^{2}}=2x\] done clear
  C)
             \[{{y}^{2}}=12x\]                        done clear
  D)
             \[{{y}^{2}}=6x\] done clear
  View Solution play_arrow

• question_answer19)
  Locus of the poles of focal chords of a parabola is of parabola [EAMCET 2002]
  A)
             The tangent at the vertex          done clear
  B)
             The axis done clear
  C)
             A focal chord                              done clear
  D)
             The directrix done clear
  View Solution play_arrow

• question_answer20)
  The parabola \[{{y}^{2}}=x\] is symmetric about  [Kerala (Engg.) 2002]
  A)
             x-axis                                          done clear
  B)
             y-axis done clear
  C)
             Both x-axis and y-axis                done clear
  D)
             The line \[y=x\] done clear
  View Solution play_arrow

• question_answer21)
  The point on the parabola \[{{y}^{2}}=18x\], for which the ordinate is three times the abscissa, is [MP PET 2003]
  A)
             (6, 2)                                          done clear
  B)
             (?2, ?6) done clear
  C)
             (3, 18)                                        done clear
  D)
             (2, 6) done clear
  View Solution play_arrow

• question_answer22)
  The equation of latus rectum of a parabola is \[x+y=8\] and the equation of the tangent at the vertex is \[x+y=12\], then length of the latus rectum is                                                                                            [MP PET 2002]
  A)
             \[4\sqrt{2}\]                              done clear
  B)
             \[2\sqrt{2}\] done clear
  C)
             8      done clear
  D)
             \[8\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer23)
   Vertex of the parabola \[{{y}^{2}}+2y+x=0\] lies in the quadrant [MP PET 1989]
  A)
             First                                            done clear
  B)
             Second                                       done clear
  C)
             Third                                           done clear
  D)
             Fourth done clear
  View Solution play_arrow

• question_answer24)
  The equation \[{{x}^{2}}-2xy+{{y}^{2}}+3x+2=0\] represents  [UPSEAT 2001]
  A)
             A parabola                                 done clear
  B)
             An ellipse done clear
  C)
             A hyperbola                                done clear
  D)
             A circle done clear
  View Solution play_arrow

• question_answer25)
  \[x-2={{t}^{2}},\ y=2t\] are the parametric equations of the parabola
  A)
             \[{{y}^{2}}=4x\]                          done clear
  B)
             \[{{y}^{2}}=-4x\] done clear
  C)
             \[{{x}^{2}}=-4y\]                        done clear
  D)
             \[{{y}^{2}}=4(x-2)\] done clear
  View Solution play_arrow

• question_answer26)
  The equation of the latus rectum of the parabola \[{{x}^{2}}+4x+2y=0\] is             [Pb. CET 2004]
  A)
             \[2y+3=0\]                                 done clear
  B)
             \[3y=2\] done clear
  C)
             \[2y=3\]                                     done clear
  D)
             \[3y+2=0\] done clear
  View Solution play_arrow

• question_answer27)
  Vertex of the parabola \[9{{x}^{2}}-6x+36y+9=0\] is
  A)
             \[(1/3,\ -2/9)\]                          done clear
  B)
             \[(-1/3,\ -1/2)\] done clear
  C)
             \[(-1/3,\ 1/2)\]                          done clear
  D)
             \[(1/3,\ 1/2)\] done clear
  View Solution play_arrow

• question_answer28)
  The equation of the parabola whose axis is vertical and passes through the points (0, 0), (3, 0) and       (?1, 4) is
  A)
             \[{{x}^{2}}-3x-y=0\]                   done clear
  B)
             \[{{x}^{2}}+3x+y=0\] done clear
  C)
             \[{{x}^{2}}-4x+2y=0\]                 done clear
  D)
             \[{{x}^{2}}-4x-2y=0\] done clear
  View Solution play_arrow

• question_answer29)
  The equation of the parabola whose vertex is        (­?1, ?2), axis is vertical and which passes through the point (3, 6), is
  A)
             \[{{x}^{2}}+2x-2y-3=0\]             done clear
  B)
             \[2{{x}^{2}}=3y\] done clear
  C)
             \[{{x}^{2}}-2x-y+3=0\]               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer30)
  Axis of the parabola \[{{x}^{2}}-4x-3y+10=0\] is
  A)
             \[y+2=0\]                                   done clear
  B)
             \[x+2=0\] done clear
  C)
             \[y-2=0\]                                    done clear
  D)
             \[x-2=0\] done clear
  View Solution play_arrow

• question_answer31)
  Equation of the parabola whose directrix is \[y=2x-9\] and focus (?8, ?2) is
  A)
             \[{{x}^{2}}+4{{y}^{2}}+4xy+16x+2y+259=0\] done clear
  B)
             \[{{x}^{2}}+4{{y}^{2}}+4xy+116x+2y+259=0\] done clear
  C)
             \[{{x}^{2}}+{{y}^{2}}+4xy+116x+2y+259=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer32)
  The equation of the parabola with (?3, 0) as focus and \[x+5=0\] as directirx, is   [RPET 1985, 86, 89; MP PET 1991]
  A)
             \[{{x}^{2}}=4(y+4)\]                   done clear
  B)
             \[{{x}^{2}}=4(y-4)\] done clear
  C)
             \[{{y}^{2}}=4(x+4)\]                   done clear
  D)
             \[{{y}^{2}}=4(x-4)\] done clear
  View Solution play_arrow

• question_answer33)
  The equation of the parabola whose vertex and focus lies on the x-axis at distance a and a? from the origin, is  [RPET 2000]
  A)
                               done clear
  B)
             \[{{y}^{2}}=4(a'-a)(x+a)\] done clear
  C)
             \[{{y}^{2}}=4(a'+a)(x-a)\]          done clear
  D)
             \[{{y}^{2}}=4(a'+a)(x+a)\] done clear
  View Solution play_arrow

• question_answer34)
  The focus of the parabola \[{{y}^{2}}=4y-4x\] is              [MP PET 1991]
  A)
             (0, 2)                                          done clear
  B)
             (1, 2) done clear
  C)
             (2, 0)                                          done clear
  D)
             (2, 1) done clear
  View Solution play_arrow

• question_answer35)
  Vertex of the parabola \[{{x}^{2}}+4x+2y-7=0\] is [MP PET 1990]
  A)
             (?2, 11/2)                                   done clear
  B)
             (?2, 2) done clear
  C)
             (?2, 11)                                      done clear
  D)
             (2, 11) done clear
  View Solution play_arrow

• question_answer36)
  If the axis of a parabola is horizontal and it passes through the points (0, 0), (0, ?1) and (6, 1), then its equation is
  A)
             \[{{y}^{2}}+3y-x-4=0\]               done clear
  B)
             \[{{y}^{2}}-3y+x-4=0\] done clear
  C)
             \[{{y}^{2}}-3y-x-4=0\]                done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer37)
  The equation of the latus rectum of the parabola represented by equation \[{{y}^{2}}+2Ax+2By+C=0\] is
  A)
             \[x=\frac{{{B}^{2}}+{{A}^{2}}-C}{2A}\]                                         done clear
  B)
             \[x=\frac{{{B}^{2}}-{{A}^{2}}+C}{2A}\] done clear
  C)
             \[x=\frac{{{B}^{2}}-{{A}^{2}}-C}{2A}\]                                          done clear
  D)
             \[x=\frac{{{A}^{2}}-{{B}^{2}}-C}{2A}\] done clear
  View Solution play_arrow

• question_answer38)
  The parametric equation of the curve \[{{y}^{2}}=8x\]are
  A)
             \[x={{t}^{2}},\ y=2t\]                 done clear
  B)
             \[x=2{{t}^{2}},\ y=4t\] done clear
  C)
             \[x=2t,\ y=4{{t}^{2}}\]               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer39)
  The equations \[x=\frac{t}{4},\ y=\frac{{{t}^{2}}}{4}\] represents
  A)
             A circle                                       done clear
  B)
             A parabola done clear
  C)
             An ellipse                                   done clear
  D)
             A hyperbola done clear
  View Solution play_arrow

• question_answer40)
  The equation of parabola whose vertex and focus are (0, 4) and (0, 2) respectively, is       [RPET 1987, 89, 90, 91]
  A)
             \[{{y}^{2}}-8x=32\]                    done clear
  B)
             \[{{y}^{2}}+8x=32\] done clear
  C)
             \[{{x}^{2}}+8y=32\]                    done clear
  D)
             \[{{x}^{2}}-8y=32\] done clear
  View Solution play_arrow

• question_answer41)
  Curve \[16{{x}^{2}}+8xy+{{y}^{2}}-74x-78y+212=0\] represents
  A)
             Parabola                                     done clear
  B)
             Hyperbola done clear
  C)
             Ellipse                                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer42)
  The length of the latus rectum of the parabola \[9{{x}^{2}}-6x+36y+19=0\]       [MP PET 1994]
  A)
             36    done clear
  B)
             9 done clear
  C)
             6      done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer43)
  The axis of the parabola \[9{{y}^{2}}-16x-12y-57=0\] is [MNR 1995]
  A)
             \[3y=2\]                                     done clear
  B)
             \[x+3y=3\] done clear
  C)
             \[2x=3\]                                     done clear
  D)
             \[y=3\] done clear
  View Solution play_arrow

• question_answer44)
  The vertex of a parabola is the point (a, b) and latus rectum is of length l. If the axis of the parabola is along the positive direction of y­-axis, then its equation is
  A)
             \[{{(x+a)}^{2}}=\frac{l}{2}(2y-2b)\]  done clear
  B)
             \[{{(x-a)}^{2}}=\frac{l}{2}(2y-2b)\] done clear
  C)
             \[{{(x+a)}^{2}}=\frac{l}{4}(2y-2b)\]  done clear
  D)
             \[{{(x-a)}^{2}}=\frac{l}{8}(2y-2b)\] done clear
  View Solution play_arrow

• question_answer45)
  If the vertex of the parabola \[y={{x}^{2}}-8x+c\] lies on x-axis, then the value of c is
  A)
  -16  done clear
  B)
  -4 done clear
  C)
  4      done clear
  D)
  16 done clear
  View Solution play_arrow

• question_answer46)
  The points of intersection of the curves whose parametric equations are \[x={{t}^{2}}+1,\ y=2t\] and \[x=2s,\ y=\frac{2}{s}\] is given by
  A)
             \[(1,\ -3)\]                                 done clear
  B)
             (2, 2) done clear
  C)
             (?2, 4)                                        done clear
  D)
             (1, 2) done clear
  View Solution play_arrow

• question_answer47)
  The latus rectum of the parabola \[{{y}^{2}}=5x+4y+1\]is [MP PET 1996]
  A)
             \[\frac{5}{4}\]                            done clear
  B)
             10 done clear
  C)
             5      done clear
  D)
             \[\frac{5}{2}\] done clear
  View Solution play_arrow

• question_answer48)
  The equation of the locus of a point which moves so as to be at equal distances from the point (a, 0) and the y-axis is
  A)
             \[{{y}^{2}}-2ax+{{a}^{2}}=0\]    done clear
  B)
             \[{{y}^{2}}+2ax+{{a}^{2}}=0\] done clear
  C)
             \[{{x}^{2}}-2ay+{{a}^{2}}=0\]    done clear
  D)
             \[{{x}^{2}}+2ay+{{a}^{2}}=0\] done clear
  View Solution play_arrow

• question_answer49)
  The focus of the parabola \[{{x}^{2}}=2x+2y\] is
  A)
             \[\left( \frac{3}{2},\ \frac{-1}{2} \right)\]                                    done clear
  B)
             \[\left( 1,\ \frac{-1}{2} \right)\] done clear
  C)
             (1, 0)                                          done clear
  D)
             (0, 1) done clear
  View Solution play_arrow

• question_answer50)
  Latus rectum of the parabola \[{{y}^{2}}-4y-2x-8=0\] is
  A)
             2      done clear
  B)
             4 done clear
  C)
             8      done clear
  D)
             1 done clear
  View Solution play_arrow

• question_answer51)
  The equation of the parabola with focus (a, b) and directrix \[\frac{x}{a}+\frac{y}{b}=1\] is given by               [MP PET 1997]
  A)
             \[{{(ax-by)}^{2}}-2{{a}^{3}}x-2{{b}^{3}}y+{{a}^{4}}+{{a}^{2}}{{b}^{2}}+{{b}^{4}}=0\] done clear
  B)
             \[{{(ax+by)}^{2}}-2{{a}^{3}}x-2{{b}^{3}}y-{{a}^{4}}+{{a}^{2}}{{b}^{2}}-{{b}^{4}}=0\] done clear
  C)
             \[{{(ax-by)}^{2}}+{{a}^{4}}+{{b}^{4}}-2{{a}^{3}}x=0\] done clear
  D)
             \[{{(ax-by)}^{2}}-2{{a}^{3}}x=0\] done clear
  View Solution play_arrow

• question_answer52)
  The length of latus rectum of the parabola \[4{{y}^{2}}+2x-20y+17=0\] is          [MP PET 1999]
  A)
             3      done clear
  B)
             6 done clear
  C)
             \[\frac{1}{2}\]                            done clear
  D)
             9 done clear
  View Solution play_arrow

• question_answer53)
  Eccentricity of the parabola \[{{x}^{2}}-4x-4y+4=0\] is [RPET 1996; Pb. CET 2003]
  A)
             \[e=0\]                                       done clear
  B)
             \[e=1\] done clear
  C)
             \[e>4\]                                       done clear
  D)
             \[e=4\] done clear
  View Solution play_arrow

• question_answer54)
   The vertex of the parabola \[3x-2{{y}^{2}}-4y+7=0\] is [RPET 1996]
  A)
  (3, 1)                                          done clear
  B)
  (-3, -1) done clear
  C)
  (-3, 1)                                        done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer55)
  The focus of the parabola \[4{{y}^{2}}-6x-4y=5\] is   [RPET 1997]
  A)
  (-8/5, 2)                                     done clear
  B)
  (-5/8, 1/2) done clear
  C)
  (1/2, 5/8)                                   done clear
  D)
  (5/8, -1/2) done clear
  View Solution play_arrow

• question_answer56)
  The vertex of the parabola \[{{x}^{2}}+8x+12y+4=0\] is [DCE 1999]
  A)
  (-4, 1)                                        done clear
  B)
  (4, -1) done clear
  C)
  (-4, -1)                                      done clear
  D)
  (4, 1) done clear
  View Solution play_arrow

• question_answer57)
  Focus of the parabola \[{{(y-2)}^{2}}=20(x+3)\] is  [Karnataka CET 1999]
  A)
  (3, -2)                                        done clear
  B)
  (2, -3) done clear
  C)
  (2, 2)                                          done clear
  D)
  (3, 3) done clear
  View Solution play_arrow

• question_answer58)
  The length of the latus rectum of the parabola \[{{x}^{2}}-4x-8y+12=0\] is        [MP PET 2000]
  A)
             4      done clear
  B)
             6 done clear
  C)
             8      done clear
  D)
             10 done clear
  View Solution play_arrow

• question_answer59)
  The focus of the parabola \[y=2{{x}^{2}}+x\] is               [MP PET 2000]
  A)
             (0, 0)                                          done clear
  B)
             \[\left( \frac{1}{2},\ \frac{1}{4} \right)\] done clear
  C)
             \[\left( -\frac{1}{4},\ 0 \right)\]       done clear
  D)
             \[\left( -\frac{1}{4},\ \frac{1}{8} \right)\] done clear
  View Solution play_arrow

• question_answer60)
  The focus of the parabola \[{{y}^{2}}-x-2y+2=0\]is         [UPSEAT 2000]
  A)
             \[(1/4,\ 0)\]                               done clear
  B)
             (1, 2) done clear
  C)
             (3/4, 1)                                       done clear
  D)
             (5/4,1) done clear
  View Solution play_arrow

• question_answer61)
  The vertex of parabola \[{{(y-2)}^{2}}=16(x-1)\] is  [Karnataka CET 2001]
  A)
             (2, 1)                                          done clear
  B)
             (1, ?2) done clear
  C)
             (?1, 2)                                        done clear
  D)
             (1, 2) done clear
  View Solution play_arrow

• question_answer62)
  Equation of the parabola with its vertex at (1, 1) and focus (3, 1) is [Karnataka CET 2001, 02]
  A)
             \[{{(x-1)}^{2}}=8(y-1)\]              done clear
  B)
             \[{{(y-1)}^{2}}=8(x-3)\] done clear
  C)
             \[{{(y-1)}^{2}}=8(x-1)\]              done clear
  D)
             \[{{(x-3)}^{2}}=8(y-1)\] done clear
  View Solution play_arrow

• question_answer63)
  The equation of parabola whose focus is (5, 3) and directrix is \[3x-4y+1=0\], is               [MP PET 2002]
  A)
             \[{{(4x+3y)}^{2}}-256x-142y+849=0\] done clear
  B)
             \[{{(4x-3y)}^{2}}-256x-142y+849=0\] done clear
  C)
             \[{{(3x+4y)}^{2}}-142x-256y+849=0\] done clear
  D)
             \[{{(3x-4y)}^{2}}-256x-142y+849=0\] done clear
  View Solution play_arrow

• question_answer64)
  Which of the following points lie on the parabola \[{{x}^{2}}=4ay\] [RPET 2002]
  A)
             \[x=a{{t}^{2}},\ y=2at\]             done clear
  B)
             \[x=2at,\ y=at\] done clear
  C)
             \[x=2a{{t}^{2}},\ y=at\]             done clear
  D)
             \[x=2at,\ y=a{{t}^{2}}\] done clear
  View Solution play_arrow

• question_answer65)
  The equation of the parabola whose vertex is at (2, ?1) and focus at (2, ?3) is [Kerala (Engg.) 2002]
  A)
             \[{{x}^{2}}+4x-8y-12=0\]           done clear
  B)
             \[{{x}^{2}}-4x+8y+12=0\] done clear
  C)
             \[{{x}^{2}}+8y=12\]                    done clear
  D)
             \[{{x}^{2}}-4x+12=0\] done clear
  View Solution play_arrow

• question_answer66)
  The directrix of the parabola \[{{x}^{2}}-4x-8y+12=0\] is  [Karnataka CET 2003]
  A)
             \[x=1\]                                       done clear
  B)
             \[y=0\] done clear
  C)
             \[x=-1\]                                      done clear
  D)
             \[y=-1\] done clear
  View Solution play_arrow

• question_answer67)
  The equation of the parabola with focus (0, 0) and directrix \[x+y=4\] is            [EAMCET 2003]
  A)
             \[{{x}^{2}}+{{y}^{2}}-2xy+8x+8y-16=0\] done clear
  B)
             \[{{x}^{2}}+{{y}^{2}}-2xy+8x+8y=0\] done clear
  C)
             \[{{x}^{2}}+{{y}^{2}}+8x+8y-16=0\]   done clear
  D)
             \[{{x}^{2}}-{{y}^{2}}+8x+8y-16=0\] done clear
  View Solution play_arrow

• question_answer68)
  If (0, 6) and (0, 3) are respectively the vertex and focus of a parabola, then its equation is               [Karnataka CET 2004]
  A)
             \[{{x}^{2}}+12y=72\]                  done clear
  B)
             \[{{x}^{2}}-12y=72\] done clear
  C)
             \[{{y}^{2}}-12x=72\]                  done clear
  D)
             \[{{y}^{2}}+12x=72\] done clear
  View Solution play_arrow

• question_answer69)
  The equation of the directrix of the parabola \[{{x}^{2}}+8y-2x=7\] is [UPSEAT 2004]
  A)
             \[y=3\]                                       done clear
  B)
             \[y=-3\] done clear
  C)
             \[y=2\]                                       done clear
  D)
             \[y=0\] done clear
  View Solution play_arrow

• question_answer70)
  The equation of axis of the parabola \[2{{x}^{2}}+5y-3x+4=0\] is [Pb. CET 2000]
  A)
             \[x=\frac{3}{4}\]                        done clear
  B)
             \[y=\frac{3}{4}\] done clear
  C)
             \[x=-\frac{1}{2}\]                       done clear
  D)
             \[x-3y=5\] done clear
  View Solution play_arrow

• question_answer71)
  If \[{{x}^{2}}+6x+20y-51=0\], then axis of parabola is  [Orissa JEE 2004]
  A)
             \[x+3=0\]                                   done clear
  B)
             \[x-3=0\] done clear
  C)
             \[x=1\]                                       done clear
  D)
             \[x+1=0\] done clear
  View Solution play_arrow

• question_answer72)
  The equation of the tangent to the parabola \[y={{x}^{2}}-x\] at the point where \[x=1\], is            [MP PET 1992]
  A)
             \[y=-x-1\]                                   done clear
  B)
             \[y=-x+1\] done clear
  C)
             \[y=x+1\]                                    done clear
  D)
             \[y=x-1\] done clear
  View Solution play_arrow

• question_answer73)
  The point of intersection of the latus rectum and axis of the parabola \[{{y}^{2}}+4x+2y-8=0\]
  A)
             (5/4, ?1)                                     done clear
  B)
             (9/4, ?1) done clear
  C)
             (7/2, 5/2)                                   done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer74)
  The point of contact of the tangent \[18x-6y+1=0\] to the parabola \[{{y}^{2}}=2x\]is
  A)
             \[\left( \frac{-1}{18},\ \frac{-1}{3} \right)\]                                done clear
  B)
             \[\left( \frac{-1}{18},\ \frac{1}{3} \right)\] done clear
  C)
             \[\left( \frac{1}{18},\ \frac{-1}{3} \right)\]                                  done clear
  D)
             \[\left( \frac{1}{18},\ \frac{1}{3} \right)\] done clear
  View Solution play_arrow

• question_answer75)
  The equation of the common tangent of the parabolas \[{{x}^{2}}=108y\] and \[{{y}^{2}}=32x\], is
  A)
             \[2x+3y=36\]                              done clear
  B)
             \[2x+3y+36=0\] done clear
  C)
             \[3x+2y=36\]                              done clear
  D)
             \[3x+2y+36=0\] done clear
  View Solution play_arrow

• question_answer76)
  The line \[lx+my+n=0\] will touch the parabola \[{{y}^{2}}=4ax\], if [RPET 1988; MNR 1977; MP PET 2003]
  A)
             \[mn=a{{l}^{2}}\]                       done clear
  B)
             \[lm=a{{n}^{2}}\] done clear
  C)
             \[ln=a{{m}^{2}}\]                       done clear
  D)
             \[mn=al\] done clear
  View Solution play_arrow

• question_answer77)
  The line \[x\cos \alpha +y\sin \alpha =p\] will touch the parabola \[{{y}^{2}}=4a(x+a)\], if
  A)
             \[p\cos \alpha +a=0\]               done clear
  B)
             \[p\cos \alpha -a=0\] done clear
  C)
             \[a\cos \alpha +p=0\]               done clear
  D)
             \[a\cos \alpha -p=0\] done clear
  View Solution play_arrow

• question_answer78)
  The equation of a tangent to the parabola \[{{y}^{2}}=4ax\] making an angle \[\theta \] with x-axis is
  A)
             \[y=x\cot \theta +a\tan \theta \]     done clear
  B)
             \[x=y\tan \theta +a\cot \theta \] done clear
  C)
             \[y=x\tan \theta +a\cot \theta \]     done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer79)
  The equation of the tangent to the parabola \[{{y}^{2}}=4x+5\] parallel to the line \[y=2x+7\] is     [MNR 1979]
  A)
             \[2x-y-3=0\]                               done clear
  B)
             \[2x-y+3=0\] done clear
  C)
             \[2x+y+3=0\]                              done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer80)
  The point of the contact of the tangent to the parabola \[{{y}^{2}}=4ax\] which makes an angle of \[{{60}^{o}}\]with x-axis, is
  A)
             \[\left( \frac{a}{3},\ \frac{2a}{\sqrt{3}} \right)\]                        done clear
  B)
             \[\left( \frac{2a}{\sqrt{3}},\ \frac{a}{3} \right)\] done clear
  C)
             \[\left( \frac{a}{\sqrt{3}},\ \frac{2a}{3} \right)\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer81)
  The straight line \[y=2x+\lambda \] does not meet the parabola \[{{y}^{2}}=2x\], if         [MP PET 1993; MNR 1977]
  A)
             \[\lambda <\frac{1}{4}\]           done clear
  B)
             \[\lambda >\frac{1}{4}\] done clear
  C)
             \[\lambda =4\]                          done clear
  D)
             \[\lambda =1\] done clear
  View Solution play_arrow

• question_answer82)
  The equation of the tangent at a point \[P(t)\] where ?t? is any parameter to the parabola \[{{y}^{2}}=4ax\], is             [MNR 1983]
  A)
             \[yt=x+a{{t}^{2}}\]                     done clear
  B)
             \[y=xt+a{{t}^{2}}\] done clear
  C)
             \[y=xt+\frac{a}{t}\]                    done clear
  D)
             \[y=tx\] done clear
  View Solution play_arrow

• question_answer83)
  The line \[y=2x+c\] is a tangent to the parabola \[{{y}^{2}}=16x\], if c equals    [MNR 1988]
  A)
             \[-2\]                                          done clear
  B)
             \[-1\] done clear
  C)
             0      done clear
  D)
             2 done clear
  View Solution play_arrow

• question_answer84)
  The line \[y=mx+1\] is a tangent to the parabola \[{{y}^{2}}=4x\], if [MNR 1990; Kurukshetra CEE 1998; DCE 2000; Pb. CET 2004]
  A)
             \[m=1\]                                      done clear
  B)
             \[m=2\] done clear
  C)
             \[m=4\]                                      done clear
  D)
             \[m=3\] done clear
  View Solution play_arrow

• question_answer85)
  The angle of intersection between the curves \[{{y}^{2}}=4x\] and \[{{x}^{2}}=32y\] at point (16, 8), is           [RPET 1987, 96]
  A)
             \[{{\tan }^{-1}}\left( \frac{3}{5} \right)\]                                     done clear
  B)
             \[{{\tan }^{-1}}\left( \frac{4}{5} \right)\] done clear
  C)
             \[\pi \]                                       done clear
  D)
             \[\frac{\pi }{2}\] done clear
  View Solution play_arrow

• question_answer86)
  The locus of a foot of perpendicular drawn to the tangent of parabola \[{{y}^{2}}=4ax\] from focus, is           [RPET 1989]
  A)
             \[x=0\]                                       done clear
  B)
             \[y=0\] done clear
  C)
             \[{{y}^{2}}=2a(x+a)\]                 done clear
  D)
             \[{{x}^{2}}+{{y}^{2}}(x+a)=0\] done clear
  View Solution play_arrow

• question_answer87)
  If the straight line \[x+y=1\] touches the parabola \[{{y}^{2}}-y+x=0\], then the co-ordinates of the point of contact are               [RPET 1991]
  A)
             (1, 1)                                          done clear
  B)
             \[\left( \frac{1}{2},\ \frac{1}{2} \right)\] done clear
  C)
             (0, 1)                                          done clear
  D)
             (1, 0) done clear
  View Solution play_arrow

• question_answer88)
  If the line \[y=mx+c\] is a tangent to the parabola \[{{y}^{2}}=4a(x+a)\] then \[ma+\frac{a}{m}\] is equal to
  A)
             c      done clear
  B)
             2c done clear
  C)
             ? c   done clear
  D)
             3c done clear
  View Solution play_arrow

• question_answer89)
  A tangent to the parabola \[{{y}^{2}}=8x\] makes an angle of \[{{45}^{o}}\]with the straight line \[y=3x+5\], then the equation of tangent is
  A)
             \[2x+y-1=0\]                              done clear
  B)
             \[x+2y-1=0\] done clear
  C)
             \[2x+y+1=0\]                              done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer90)
  The angle between the tangents drawn at the end points of the latus rectum of parabola \[{{y}^{2}}=4ax\], is
  A)
             \[\frac{\pi }{3}\]                        done clear
  B)
             \[\frac{2\pi }{3}\] done clear
  C)
             \[\frac{\pi }{4}\]                        done clear
  D)
             \[\frac{\pi }{2}\] done clear
  View Solution play_arrow

• question_answer91)
  The line \[y=mx+c\] touches the parabola \[{{x}^{2}}=4ay\], if  [MNR 1973; MP PET 1994, 99]
  A)
             \[c=-am\]                                   done clear
  B)
             \[c=-a/m\] done clear
  C)
             \[c=-a{{m}^{2}}\]                       done clear
  D)
             \[c=a/{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer92)
  The locus of the point of intersection of the perpendicular tangents to the parabola \[{{x}^{2}}=4ay\]is          [MP PET 1994]
  A)
             Axis of the parabola                  done clear
  B)
             Directrix of the parabola done clear
  C)
             Focal chord of the parabola      done clear
  D)
             Tangent at vertex to the parabola done clear
  View Solution play_arrow

• question_answer93)
  The angle between the tangents drawn from the origin to the parabola \[{{y}^{2}}=4a(x-a)\] is      [MNR 1994]
  A)
             \[{{90}^{o}}\]                             done clear
  B)
             \[{{30}^{o}}\] done clear
  C)
             \[{{\tan }^{-1}}\frac{1}{2}\]      done clear
  D)
             \[{{45}^{o}}\] done clear
  View Solution play_arrow

• question_answer94)
  If line \[x=my+k\] touches the parabola \[{{x}^{2}}=4ay\], then \[k=\] [MP PET 1995]
  A)
             \[\frac{a}{m}\]                          done clear
  B)
             am done clear
  C)
             \[a{{m}^{2}}\]                            done clear
  D)
             \[-a{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer95)
  If \[{{y}_{1}},\ {{y}_{2}}\] are the ordinates of two points P and Q on the parabola and \[{{y}_{3}}\] is the ordinate of the point of intersection of tangents at P and Q, then
  A)
             \[{{y}_{1}},\ {{y}_{2}},\ {{y}_{3}}\] are in A.P.                               done clear
  B)
             \[{{y}_{1}},\ {{y}_{3}},\ {{y}_{2}}\] are in A.P. done clear
  C)
             \[{{y}_{1}},\ {{y}_{2}},\ {{y}_{3}}\] are in G.P.                              done clear
  D)
             \[{{y}_{1}},\ {{y}_{3}},\ {{y}_{2}}\] are in G.P. done clear
  View Solution play_arrow

• question_answer96)
  The two parabolas \[{{y}^{2}}=4x\] and \[{{x}^{2}}=4y\] intersect at a point P, whose abscissa is not zero, such that
  A)
             They both touch each other at P done clear
  B)
             They cut at right angles at P done clear
  C)
             The tangents to each curve at P make complementary angles with the x-axis done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer97)
   The line \[y=2x+c\] is tangent to the parabola \[{{y}^{2}}=4x\], then \[c=\]      [MP PET 1996]
  A)
             \[-\frac{1}{2}\]                          done clear
  B)
             \[\frac{1}{2}\] done clear
  C)
             \[\frac{1}{3}\]                            done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer98)
  The condition for which the straight line \[y=mx+c\] touches the parabola \[{{y}^{2}}=4ax\] is        [MP PET 1997, 2001]
  A)
             \[a=c\]                                       done clear
  B)
             \[\frac{a}{c}=m\] done clear
  C)
             \[m={{a}^{2}}c\]                        done clear
  D)
             \[m=a{{c}^{2}}\] done clear
  View Solution play_arrow

• question_answer99)
  If the parabola \[{{y}^{2}}=4ax\] passes through the point (1, ?2), then the tangent at this point is                 [MP PET 1998]
  A)
             \[x+y-1=0\]                                done clear
  B)
             \[x-y-1=0\] done clear
  C)
             \[x+y+1=0\]                                done clear
  D)
             \[x-y+1=0\] done clear
  View Solution play_arrow

• question_answer100)
  The equation of the tangent to the parabola \[{{y}^{2}}=16x\], which is perpendicular to the line \[y=3x+7\] is               [MP PET 1998]
  A)
             \[y-3x+4=0\]                              done clear
  B)
             \[3y-x+36=0\] done clear
  C)
             \[3y+x-36=0\]                            done clear
  D)
             \[3y+x+36=0\] done clear
  View Solution play_arrow

• question_answer101)
  The equation of the tangent to the parabola \[{{y}^{2}}=4ax\] at point \[(a/{{t}^{2}},\ 2a/t)\] is     [RPET 1996]
  A)
  \[ty=x{{t}^{2}}+a\]                                done clear
  B)
  \[ty=x+a{{t}^{2}}\] done clear
  C)
  \[y=tx+a{{t}^{2}}\]                                done clear
  D)
  \[y=tx+(a/{{t}^{2}})\] done clear
  View Solution play_arrow

• question_answer102)
  The equation of common tangent to the circle \[{{x}^{2}}+{{y}^{2}}=2\] and parabola \[{{y}^{2}}=8x\] is        [RPET 1997]
  A)
             \[y=x+1\]                                    done clear
  B)
             \[y=x+2\] done clear
  C)
             \[y=x-2\]                                    done clear
  D)
             \[y=-x+2\] done clear
  View Solution play_arrow

• question_answer103)
  If the line \[lx+my+n=0\] is a tangent to the parabola \[{{y}^{2}}=4ax\], then locus of its point of contact is   [RPET 1997]
  A)
             A straight line                            done clear
  B)
             A circle done clear
  C)
             A parabola                                 done clear
  D)
             Two straight lines done clear
  View Solution play_arrow

• question_answer104)
  The line \[x-y+2=0\] touches the parabola \[{{y}^{2}}=8x\] at the point              [Roorkee 1998]
  A)
             \[(2,\ -4)\]                                 done clear
  B)
             \[(1,\ 2\sqrt{2})\] done clear
  C)
             \[(4,\ -4\sqrt{2})\]                     done clear
  D)
             (2, 4) done clear
  View Solution play_arrow

• question_answer105)
  The tangent to the parabola \[{{y}^{2}}=4ax\] at the point (a, 2a) makes with x-axis an angle equal to           [SCRA 1996]
  A)
             \[\frac{\pi }{3}\]                        done clear
  B)
             \[\frac{\pi }{4}\] done clear
  C)
             \[\frac{\pi }{2}\]                        done clear
  D)
             \[\frac{\pi }{6}\] done clear
  View Solution play_arrow

• question_answer106)
  If \[lx+my+n=0\] is tangent to the parabola \[{{x}^{2}}=y\], then condition of tangency is                [RPET 1999]
  A)
             \[{{l}^{2}}=2mn\]                       done clear
  B)
             \[l=4{{m}^{2}}{{n}^{2}}\] done clear
  C)
             \[{{m}^{2}}=4ln\]                       done clear
  D)
             \[{{l}^{2}}=4mn\] done clear
  View Solution play_arrow

• question_answer107)
  The equation of the tangent to the parabola \[{{y}^{2}}=9x\] which goes through the point (4, 10), is             [MP PET 2000]
  A)
             \[x+4y+1=0\]                              done clear
  B)
             \[9x+4y+4=0\] done clear
  C)
             \[x-4y+36=0\]                            done clear
  D)
             \[9x-4y+4=0\] done clear
  View Solution play_arrow

• question_answer108)
  . Two perpendicular tangents to \[{{y}^{2}}=4ax\] always intersect on the line, if               [Karnataka CET 2000]
  A)
             \[x=a\]                                       done clear
  B)
             \[x+a=0\] done clear
  C)
             \[x+2a=0\]                                 done clear
  D)
             \[x+4a=0\] done clear
  View Solution play_arrow

• question_answer109)
  The equation of the common tangent touching the circle \[{{(x-3)}^{2}}+{{y}^{2}}=9\] and the parabola \[{{y}^{2}}=4x\] above the x-axis, is [IIT Screening 2001]
  A)
             \[\sqrt{3}y=3x+1\]                     done clear
  B)
             \[\sqrt{3}y=-(x+3)\] done clear
  C)
             \[\sqrt{3}y=x+3\]                       done clear
  D)
             \[\sqrt{3}y=-(3x+1)\] done clear
  View Solution play_arrow

• question_answer110)
  The point at which the line \[y=mx+c\] touches the parabola \[{{y}^{2}}=4ax\] is              [RPET 2001]
  A)
             \[\left( \frac{a}{{{m}^{2}}},\ \frac{2a}{m} \right)\]                    done clear
  B)
             \[\left( \frac{a}{{{m}^{2}}},\ \frac{-2a}{m} \right)\] done clear
  C)
             \[\left( -\frac{a}{{{m}^{2}}},\ \frac{2a}{m} \right)\]                   done clear
  D)
             \[\left( -\frac{a}{{{m}^{2}}},\ -\frac{2a}{m} \right)\] done clear
  View Solution play_arrow

• question_answer111)
  The tangent drawn at any point P to the parabola \[{{y}^{2}}=4ax\] meets the directrix at the point K, then the angle which KP subtends at its focus is                                                                                      [RPET 1996, 2002]
  A)
             30o  done clear
  B)
             45o done clear
  C)
             60o  done clear
  D)
             90o done clear
  View Solution play_arrow

• question_answer112)
  The point of intersection of the parabola at the points \[{{t}_{1}}\] and \[{{t}_{2}}\] is     [RPET 2002]
  A)
             \[(a{{t}_{1}}{{t}_{2}},\ a({{t}_{1}}+{{t}_{2}}))\]                            done clear
  B)
             \[(2a{{t}_{1}}{{t}_{2}},\ a({{t}_{1}}+{{t}_{2}}))\] done clear
  C)
             \[(2a{{t}_{1}}{{t}_{2}},\ 2a({{t}_{1}}+{{t}_{2}}))\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer113)
  . The angle of intersection between the curves \[{{x}^{2}}=4(y+1)\] and \[{{x}^{2}}=-4(y+1)\] is        [UPSEAT 2002]
  A)
             \[\frac{\pi }{6}\]                        done clear
  B)
             \[\frac{\pi }{4}\] done clear
  C)
             0      done clear
  D)
             \[\frac{\pi }{2}\] done clear
  View Solution play_arrow

• question_answer114)
  Angle between two curves \[{{y}^{2}}=4(x+1)\] and \[{{x}^{2}}=4(y+1)\] is        [UPSEAT 2002]
  A)
             0o    done clear
  B)
             90o done clear
  C)
             60o  done clear
  D)
             30o done clear
  View Solution play_arrow

• question_answer115)
  If The tangent to the parabola \[{{y}^{2}}=ax\] makes an angle of 45o with x-axis, then the point of contact is   [RPET 1985, 90, 2003]
  A)
             \[\left( \frac{a}{2},\ \frac{a}{2} \right)\]                                     done clear
  B)
             \[\left( \frac{a}{4},\ \frac{a}{4} \right)\] done clear
  C)
             \[\left( \frac{a}{2},\ \frac{a}{4} \right)\]                                     done clear
  D)
             \[\left( \frac{a}{4},\ \frac{a}{2} \right)\] done clear
  View Solution play_arrow

• question_answer116)
  Tangents at the extremities of any focal chord of a parabola intersect
  A)
             At right angles                           done clear
  B)
             On the directrix done clear
  C)
             On the tangents at vertex done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer117)
  The point of intersection of tangents at the ends of the latus-rectum of the parabola \[{{y}^{2}}=4x\] is equal to          [Pb. CET 2003]
  A)
             (1, 0)                                          done clear
  B)
             (?1, 0) done clear
  C)
             (0, 1)                                          done clear
  D)
             (0, ?1) done clear
  View Solution play_arrow

• question_answer118)
  The angle between the tangents drawn from the points (1,4) to the parabola \[{{y}^{2}}=4x\] is     [IIT Screening 2004]
  A)
             \[\frac{\pi }{2}\]                        done clear
  B)
             \[\frac{\pi }{3}\] done clear
  C)
             \[\frac{\pi }{4}\]                        done clear
  D)
             \[\frac{\pi }{6}\] done clear
  View Solution play_arrow

• question_answer119)
  The locus of the middle points of the chords of the parabola \[{{y}^{2}}=4ax\]which passes through the origin [RPET 1997; UPSEAT 1999]
  A)
             \[{{y}^{2}}=ax\]                          done clear
  B)
             \[{{y}^{2}}=2ax\] done clear
  C)
             \[{{y}^{2}}=4ax\]                        done clear
  D)
             \[{{x}^{2}}=4ay\] done clear
  View Solution play_arrow

• question_answer120)
  The point on the parabola \[{{y}^{2}}=8x\] at which the normal is parallel to the line \[x-2y+5=0\] is
  A)
             \[(-1/2,\ 2)\]                              done clear
  B)
             \[(1/2,\ -2)\] done clear
  C)
             \[(2,\ -1/2)\]                              done clear
  D)
             \[(-2,\ 1/2)\] done clear
  View Solution play_arrow

• question_answer121)
  The maximum number of normal that can be drawn from a point to a parabola is           [MP PET 1990]
  A)
             0      done clear
  B)
             1 done clear
  C)
             2      done clear
  D)
             3 done clear
  View Solution play_arrow

• question_answer122)
  The point on the parabola \[{{y}^{2}}=8x\] at which the normal is inclined at 60o to the x-axis  has the co-ordinates      [MP PET 1993]
  A)
             \[(6,\ -4\sqrt{3})\]                     done clear
  B)
             \[(6,\ 4\sqrt{3})\] done clear
  C)
             \[(-6,\ -4\sqrt{3})\]                   done clear
  D)
             \[(-6,\ 4\sqrt{3})\] done clear
  View Solution play_arrow

• question_answer123)
  The slope of the normal at the point \[(a{{t}^{2}},\ 2at)\] of the parabola \[{{y}^{2}}=4ax\], is            [MNR 1991; UPSEAT 2000]
  A)
             \[\frac{1}{t}\]                            done clear
  B)
             t done clear
  C)
             ?t    done clear
  D)
             \[-\frac{1}{t}\] done clear
  View Solution play_arrow

• question_answer124)
  The equation of the normal at the point \[\left( \frac{a}{4},\ a \right)\] to the parabola \[{{y}^{2}}=4ax\], is [RPET 1984]
  A)
             \[4x+8y+9a=0\]                          done clear
  B)
             \[4x+8y-9a=0\] done clear
  C)
             \[4x+y-a=0\]                              done clear
  D)
             \[4x-y+a=0\] done clear
  View Solution play_arrow

• question_answer125)
  The equation of normal to the parabola at the point \[\left( \frac{a}{{{m}^{2}}},\ \frac{2a}{m} \right)\],is     [RPET 1987]
  A)
             \[y={{m}^{2}}x-2mx-a{{m}^{3}}\]     done clear
  B)
             \[{{m}^{3}}y={{m}^{2}}x-2a{{m}^{2}}-a\] done clear
  C)
             \[{{m}^{3}}y=2a{{m}^{2}}-{{m}^{2}}x+a\]                                    done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer126)
  If the line \[2x+y+k=0\] is normal to the parabola \[{{y}^{2}}=-8x\],  then the value of k will be       [RPET 1986, 97]
  A)
             \[-16\]                                        done clear
  B)
             \[-8\] done clear
  C)
             \[-24\]                                        done clear
  D)
             24 done clear
  View Solution play_arrow

• question_answer127)
  If a normal drawn to the parabola \[{{y}^{2}}=4ax\] at the point \[(a,\ 2a)\] meets parabola again on \[(a{{t}^{2}},\ 2at)\], then the value of t will be [RPET 1990]
  A)
             1      done clear
  B)
             3 done clear
  C)
             ?1    done clear
  D)
             ?3 done clear
  View Solution play_arrow

• question_answer128)
  In the parabola \[{{y}^{2}}=6x\], the equation of the chord through vertex and negative end of latus rectum, is
  A)
             \[y=2x\]                                      done clear
  B)
             \[y+2x=0\] done clear
  C)
             \[x=2y\]                                      done clear
  D)
             \[x+2y=0\] done clear
  View Solution play_arrow

• question_answer129)
  The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola \[{{y}^{2}}=8x\], is              [MNR 1976]
  A)
             \[\frac{1}{2}\sqrt{41}\]             done clear
  B)
             \[\sqrt{41}\] done clear
  C)
             \[\frac{3}{2}\sqrt{41}\]             done clear
  D)
             \[2\sqrt{41}\] done clear
  View Solution play_arrow

• question_answer130)
  If ?a? and ?c? are the segments of a focal chord of a parabola and b the semi-latus rectum, then      [MP PET 1995]
  A)
             a, b, c are in A.P.                        done clear
  B)
             a, b, c are in G.P. done clear
  C)
             a, b, c are in H.P.                       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer131)
  If the segment intercepted by the parabola \[{{y}^{2}}=4ax\] with the line \[lx+my+n=0\] subtends a right angle at the vertex, then
  A)
             \[4al+n=0\]                                done clear
  B)
             \[4al+4am+n=0\] done clear
  C)
             \[4am+n=0\]                              done clear
  D)
             \[al+n=0\] done clear
  View Solution play_arrow

• question_answer132)
  A set of parallel chords of the parabola \[{{y}^{2}}=4ax\] have their mid-point on
  A)
             Any straight line through the vertex done clear
  B)
             Any straight line through the focus done clear
  C)
             Any straight line parallel to the axis done clear
  D)
             Another parabola done clear
  View Solution play_arrow

• question_answer133)
  The equations of the normals at the ends of latus rectum of the parabola \[{{y}^{2}}=4ax\] are given by
  A)
             \[{{x}^{2}}-{{y}^{2}}-6ax+9{{a}^{2}}=0\] done clear
  B)
             \[{{x}^{2}}-{{y}^{2}}-6ax-6ay+9{{a}^{2}}=0\] done clear
  C)
             \[{{x}^{2}}-{{y}^{2}}-6ay+9{{a}^{2}}=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer134)
  If the normals at two points P and Q of a parabola \[{{y}^{2}}=4ax\] intersect at a third point R on the curve, then the product of ordinates of P and Q is
  A)
             \[4{{a}^{2}}\]                             done clear
  B)
             \[2{{a}^{2}}\] done clear
  C)
             \[-4{{a}^{2}}\]                            done clear
  D)
             \[8{{a}^{2}}\] done clear
  View Solution play_arrow

• question_answer135)
  If \[x=my+c\]is a normal to the parabola \[{{x}^{2}}=4ay\], then the value of c is
  A)
             \[-2am-a{{m}^{3}}\]                  done clear
  B)
             \[2am+a{{m}^{3}}\] done clear
  C)
             \[-\frac{2a}{m}-\frac{a}{{{m}^{3}}}\]                                           done clear
  D)
             \[\frac{2a}{m}+\frac{a}{{{m}^{3}}}\] done clear
  View Solution play_arrow

• question_answer136)
   If PSQ is the focal chord of the parabola \[{{y}^{2}}=8x\] such that\[SP=6\]. Then the length SQ is
  A)
             6      done clear
  B)
             4 done clear
  C)
             3      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer137)
  At what point on the parabola \[{{y}^{2}}=4x\], the normal makes equal angles with the co-ordinate axes     [RPET 1994]
  A)
             (4, 4)                                          done clear
  B)
             (9, 6) done clear
  C)
             (4, ?4)                                        done clear
  D)
             (1, ?2) done clear
  View Solution play_arrow

• question_answer138)
  Equation of any normal to the parabola \[{{y}^{2}}=4a(x-a)\] is
  A)
             \[y=mx-2am-a{{m}^{3}}\]         done clear
  B)
             \[y=m\,(x+a)-2am-a{{m}^{3}}\] done clear
  C)
             \[y=m\,(x-a)+\frac{a}{m}\] done clear
  D)
             \[y=m\,(x-a)-2am-a{{m}^{3}}\] done clear
  View Solution play_arrow

• question_answer139)
  Tangents drawn at the ends of any focal chord of a parabola \[{{y}^{2}}=4ax\] intersect in the line
  A)
             \[y-a=0\]                                    done clear
  B)
             \[y+a=0\] done clear
  C)
             \[x-a=0\]                                    done clear
  D)
             \[x+a=0\] done clear
  View Solution play_arrow

• question_answer140)
  The centroid of the triangle formed by joining the feet of the normals drawn from any point to the parabola \[{{y}^{2}}=4ax\], lies on [MP PET 1999]
  A)
             Axis                                            done clear
  B)
             Directrix done clear
  C)
             Latus rectum                              done clear
  D)
             Tangent at vertex done clear
  View Solution play_arrow

• question_answer141)
  If the normal to\[{{y}^{2}}=12x\] at (3, 6) meets the parabola again in (27, ?18) and the circle on the normal chord as diameter is [Kurukshetra CEE 1998]
  A)
             \[{{x}^{2}}+{{y}^{2}}+30x+12y-27=0\] done clear
  B)
             \[{{x}^{2}}+{{y}^{2}}+30x+12y+27=0\] done clear
  C)
             \[{{x}^{2}}+{{y}^{2}}-30x-12y-27=0\] done clear
  D)
             \[{{x}^{2}}+{{y}^{2}}-30x+12y-27=0\] done clear
  View Solution play_arrow

• question_answer142)
  The length of the normal chord to the parabola \[{{y}^{2}}=4x\], which subtends right angle at the vertex is [RPET 1999]
  A)
             \[6\sqrt{3}\]                              done clear
  B)
             \[3\sqrt{3}\] done clear
  C)
             2      done clear
  D)
             1 done clear
  View Solution play_arrow

• question_answer143)
  If \[x+y=k\] is a normal to the parabola \[{{y}^{2}}=12x\], then k is [IIT Screening 2000]
  A)
             3      done clear
  B)
             9 done clear
  C)
             ?9    done clear
  D)
             ?3 done clear
  View Solution play_arrow

• question_answer144)
  The normal at the point \[(bt_{1}^{2},\ 2b{{t}_{1}})\] on a parabola meets the parabola again in the point \[(bt_{2}^{2},\ 2b{{t}_{2}})\], then [MNR 1986; RPET 2003; AIEEE 2003]
  A)
             \[{{t}_{2}}=-{{t}_{1}}-\frac{2}{{{t}_{1}}}\]                                     done clear
  B)
             \[{{t}_{2}}=-{{t}_{1}}+\frac{2}{{{t}_{1}}}\] done clear
  C)
             \[{{t}_{2}}={{t}_{1}}-\frac{2}{{{t}_{1}}}\]                                      done clear
  D)
             \[{{t}_{2}}={{t}_{1}}+\frac{2}{{{t}_{1}}}\] done clear
  View Solution play_arrow

• question_answer145)
  The focal chord to \[{{y}^{2}}=16x\] is tangent to \[{{(x-6)}^{2}}+{{y}^{2}}=2\], then the possible value of the slope of this chord, are  [IIT Screening 2003]
  A)
             \[\{-1,\ 1\}\]                              done clear
  B)
             {?2, 2} done clear
  C)
             {-2, 1/2}                                     done clear
  D)
             {2, ?1/2} done clear
  View Solution play_arrow

• question_answer146)
  The normal to the parabola \[{{y}^{2}}=8x\] at the point (2, 4) meets the parabola again at the point            [Orissa JEE 2003]
  A)
             {?18, ?12}                                  done clear
  B)
             {?18, 12} done clear
  C)
             {18, 12}                                      done clear
  D)
             (18, ?12) done clear
  View Solution play_arrow

• question_answer147)
  The polar of focus of parabola                                              [RPET 1999]
  A)
             x-axis                                          done clear
  B)
             y-axis done clear
  C)
             Directrix                                     done clear
  D)
             Latus rectum done clear
  View Solution play_arrow

• question_answer148)
  Equation of diameter of parabola \[{{y}^{2}}=x\] corresponding to the chord \[x-y+1=0\] is             [RPET 2003]
  A)
             \[2y=3\]                                     done clear
  B)
             \[2y=1\] done clear
  C)
             \[2y=5\]                                     done clear
  D)
             \[y=1\] done clear
  View Solution play_arrow

• question_answer149)
  The area of the triangle formed by the lines joining the vertex of the parabola \[{{x}^{2}}=12y\] to the ends of its latus rectum is
  A)
             12 sq. unit                                  done clear
  B)
             16 sq. unit done clear
  C)
             18 sq. unit                                  done clear
  D)
             24 sq. unit done clear
  View Solution play_arrow

• question_answer150)
  The area of triangle formed inside the parabola \[{{y}^{2}}=4x\] and whose ordinates of vertices are 1, 2 and 4 will be [RPET 1990]
  A)
             \[\frac{7}{2}\]                            done clear
  B)
             \[\frac{5}{2}\] done clear
  C)
             \[\frac{3}{2}\]                            done clear
  D)
             \[\frac{3}{4}\] done clear
  View Solution play_arrow

• question_answer151)
  An equilateral triangle is inscribed in the parabola \[{{y}^{2}}=4ax\] whose vertices are at the parabola, then the length of its side is equal to
  A)
             8a    done clear
  B)
             \[8a\sqrt{3}\] done clear
  C)
             \[a\sqrt{2}\]                              done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer152)
  The ordinates of the triangle inscribed in parabola \[{{y}^{2}}=4ax\] are \[{{y}_{1}},\ {{y}_{2}},\ {{y}_{3}}\], then the area of triangle is
  A)
             \[\frac{1}{8a}({{y}_{1}}+{{y}_{2}})({{y}_{2}}+{{y}_{3}})({{y}_{3}}+{{y}_{1}})\] done clear
  B)
             \[\frac{1}{4a}({{y}_{1}}+{{y}_{2}})({{y}_{2}}+{{y}_{3}})({{y}_{3}}+{{y}_{1}})\] done clear
  C)
             \[\frac{1}{8a}({{y}_{1}}-{{y}_{2}})({{y}_{2}}-{{y}_{3}})({{y}_{3}}-{{y}_{1}})\] done clear
  D)
             \[\frac{1}{4a}({{y}_{1}}-{{y}_{2}})({{y}_{2}}-{{y}_{3}})({{y}_{3}}-{{y}_{1}})\] done clear
  View Solution play_arrow

• question_answer153)
  From the point (?1, 2) tangent lines are drawn to the parabola \[{{y}^{2}}=4x\], then the equation of chord of contact is [Roorkee 1994]
  A)
             \[y=x+1\]                                    done clear
  B)
             \[y=x-1\] done clear
  C)
             \[y+x=1\]                                    done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer154)
  For the above problem, the area of triangle formed by chord of contact and the tangents is given by              [Roorkee 1994]
  A)
             8      done clear
  B)
             \[8\sqrt{3}\] done clear
  C)
             \[8\sqrt{2}\]                              done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer155)
  The point on parabola \[2y={{x}^{2}}\], which is nearest to the point (0, 3) is                                    [J & K 2005]
  A)
             (±4, 8)                                        done clear
  B)
             \[(\pm 1,\,1/2)\] done clear
  C)
             (±2, 2)                                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer156)
  From the point (?1, ?60) two tangents are drawn to the parabola \[{{y}^{2}}=4x\]. Then the angle between the two tangents is [J & K 2005]
  A)
             30°  done clear
  B)
             45° done clear
  C)
             60°  done clear
  D)
             90° done clear
  View Solution play_arrow

• question_answer157)
  The ends of the latus rectum of the conic \[{{x}^{2}}+10x-16y+25=0\] are                                         [Karnataka CET 2005]
  A)
             (3, ?4), (13, 4)                            done clear
  B)
             (?3, ?4), (13, ?4) done clear
  C)
             (3, 4), (?13, 4)                            done clear
  D)
             (5, ?8), (?5, 8) done clear
  View Solution play_arrow

• question_answer158)
  Tangent to the parabola \[y={{x}^{2}}+6\] at (1, 7) touches the circle \[{{x}^{2}}+{{y}^{2}}+16x+12y+c=0\] at the point  [IIT Screening 2005]
  A)
             (?6, ?9)                                      done clear
  B)
             (?13, ?9) done clear
  C)
             (?6, ?7)                                      done clear
  D)
             (13, 7) done clear
  View Solution play_arrow

• question_answer159)
  The angle of intersection between the curves \[{{x}^{2}}=8y\] and \[{{y}^{2}}=8x\] at origin is                                        [RPET 1997]
  A)
             p/4  done clear
  B)
             p/3 done clear
  C)
             p/6  done clear
  D)
             p/2 done clear
  View Solution play_arrow

• question_answer160)
  If the line \[y=2x+k\] is a tangent to the curve \[{{x}^{2}}=4y\], then k is equal to                                             [AMU 2002]
  A)
             4      done clear
  B)
             1/2 done clear
  C)
             ?4    done clear
  D)
             ?1/2 done clear
  View Solution play_arrow

• question_answer161)
  The equation to a parabola which passes through the intersection of a straight line \[x+y=0\] and the circle \[{{x}^{2}}+{{y}^{2}}+4y=0\] is [Orissa JEE 2005]
  A)
             \[{{y}^{2}}=4x\]                          done clear
  B)
             \[{{y}^{2}}=x\] done clear
  C)
             \[{{y}^{2}}=2x\]                         done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer162)
  Let a circle tangent to the directrix of a parabola \[{{y}^{2}}=2ax\] has its centre coinciding with the focus of the parabola. Then the point of intersection of the parabola and circle is                                          [Orissa JEE 2005]
  A)
             (a, ?a)                                        done clear
  B)
             \[(a/2,\ a/2)\] done clear
  C)
             \[(a/2,\ \pm a)\]                       done clear
  D)
             \[(\pm a,\ a/2)\] done clear
  View Solution play_arrow

• question_answer163)
  The length intercepted by the curve \[{{y}^{2}}=4x\] on the line satisfying \[dy/dx=1\] and passing through point (0, 1) is given by [Orissa JEE 2005]
  A)
             1      done clear
  B)
             2 done clear
  C)
             0      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer164)
  The equation of a straight line drawn through the focus of the parabola \[{{y}^{2}}=-4x\] at an angle of 120° to the x-axis is [Orissa JEE 2005]
  A)
             \[y+\sqrt{3}(x-1)=0\]                 done clear
  B)
             \[y-\sqrt{3}(x-1)=0\] done clear
  C)
             \[y+\sqrt{3}(x+1)=0\]                done clear
  D)
             \[y-\sqrt{3}(x+1)=0\] done clear
  View Solution play_arrow

• question_answer165)
  The number of parabolas that can be drawn if two ends of the latus rectum are given                                     [DCE 2005]
  A)
             1      done clear
  B)
             2 done clear
  C)
             4      done clear
  D)
             3 done clear
  View Solution play_arrow

• question_answer166)
  The normal meet the parabola \[{{y}^{2}}=4ax\] at that point where the abissiae of the point is equal to the ordinate of the point is [DCE 2005]
  A)
             \[(6a,\ -9a)\]                             done clear
  B)
             \[(-9a,\ 6a)\] done clear
  C)
             \[(-6a,\ 9a)\]                             done clear
  D)
             \[(9a,\ -6a)\] done clear
  View Solution play_arrow