JEE Main & Advanced Mathematics Circle and System of Circles Question Bank

done Tangent and normal to a circle Total Questions - 120

• question_answer1)
  If the length of tangent drawn from the point (5, 3) to the circle \[{{x}^{2}}+{{y}^{2}}+2x+ky+17=0\]be 7, then k =
  A)
             4     done clear
  B)
             - 4 done clear
  C)
             - 6   done clear
  D)
             13/2 done clear
  View Solution play_arrow

• question_answer2)
  The line \[lx+my+n=0\]will be a tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]if                          [MNR 1974; AMU 1981]
  A)
             \[{{n}^{2}}({{l}^{2}}+{{m}^{2}})={{a}^{2}}\]       done clear
  B)
             \[{{a}^{2}}({{l}^{2}}+{{m}^{2}})={{n}^{2}}\] done clear
  C)
             \[n(l+m)a\]                                done clear
  D)
             \[a(l+m)=n\] done clear
  View Solution play_arrow

• question_answer3)
  The angle between the two tangents from the origin to the circle \[{{(x-7)}^{2}}+{{(y+1)}^{2}}=25\] is [MNR 1990; RPET 1997; DCE 2000]
  A)
             0     done clear
  B)
             \[\frac{\pi }{3}\] done clear
  C)
             \[\frac{\pi }{6}\]                        done clear
  D)
             \[\frac{\pi }{2}\] done clear
  View Solution play_arrow

• question_answer4)
  A pair of tangents are drawn from the origin to the circle\[{{x}^{2}}+{{y}^{2}}+20(x+y)+20=0\]. The equation of the pair of tangents is [MP PET 1990]
  A)
             \[{{x}^{2}}+{{y}^{2}}+10xy=0\]                                    done clear
  B)
             \[{{x}^{2}}+{{y}^{2}}+5xy=0\] done clear
  C)
             \[2{{x}^{2}}+2{{y}^{2}}+5xy=0\]                                  done clear
  D)
             \[2{{x}^{2}}+2{{y}^{2}}-5xy=0\] done clear
  View Solution play_arrow

• question_answer5)
  If OA and OB be the tangents to the circle \[{{x}^{2}}+{{y}^{2}}-6x-8y+21=0\]drawn from the origin O,  then AB =
  A)
             11   done clear
  B)
             \[\frac{4}{5}\sqrt{21}\] done clear
  C)
             \[\sqrt{\frac{17}{3}}\]             done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer6)
  Equation of the pair of tangents drawn from the origin to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]is
  A)
             \[gx+fy+c({{x}^{2}}+{{y}^{2}})\]                                    done clear
  B)
             \[{{(gx+fy)}^{2}}={{x}^{2}}+{{y}^{2}}\] done clear
  C)
             \[{{(gx+fy)}^{2}}={{c}^{2}}({{x}^{2}}+{{y}^{2}})\]           done clear
  D)
             \[{{(gx+fy)}^{2}}=c({{x}^{2}}+{{y}^{2}})\] done clear
  View Solution play_arrow

• question_answer7)
  If the line \[y=mx+c\]be a tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], then the point of contact is
  A)
             \[\left( \frac{-{{a}^{2}}}{c},{{a}^{2}} \right)\]                   done clear
  B)
             \[\left( \frac{{{a}^{2}}}{c},\frac{-{{a}^{2}}m}{c} \right)\] done clear
  C)
             \[\left( \frac{-{{a}^{2}}m}{c},\frac{{{a}^{2}}}{c} \right)\]             done clear
  D)
             \[\left( \frac{-{{a}^{2}}c}{m},\frac{{{a}^{2}}}{m} \right)\] done clear
  View Solution play_arrow

• question_answer8)
  The locus of the centre of a circle which passes through the point (a, 0) and touches the line \[x+1=0\], is
  A)
             Circle                                         done clear
  B)
             Ellipse done clear
  C)
             Parabola                                    done clear
  D)
             Hyperbola done clear
  View Solution play_arrow

• question_answer9)
  A point inside the circle \[{{x}^{2}}+{{y}^{2}}+3x-3y+2=0\]is  [MP PET 1988]
  A)
             (- 1, 3)                                       done clear
  B)
             (- 2, 1) done clear
  C)
             (2, 1)                                          done clear
  D)
             (- 3, 2) done clear
  View Solution play_arrow

• question_answer10)
  Position of the point (1, 1) with respect to the circle \[{{x}^{2}}+{{y}^{2}}-x+y-1=0\] is                                  [MP PET 1986, 90]
  A)
             Outside the circle                      done clear
  B)
             Upon the circle done clear
  C)
             Inside the circle                         done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer11)
  The equations of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}=50\]at the points where the line \[x+7=0\]meets it, are
  A)
             \[7x\pm y+50=0\]                   done clear
  B)
             \[7x\pm y-5=0\] done clear
  C)
             \[y\pm 7x+5=0\]                     done clear
  D)
             \[y\pm 7x-5=0\] done clear
  View Solution play_arrow

• question_answer12)
  If the line \[y=\sqrt{3}x+k\] touches the circle \[{{x}^{2}}+{{y}^{2}}=16\],  then k =
  A)
             0     done clear
  B)
             2 done clear
  C)
             4     done clear
  D)
             8 done clear
  View Solution play_arrow

• question_answer13)
  The equations of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}-6x+4y=12\]which are parallel to the straight line \[4x+3y+5=0\], are   [ISM Dhanbad 1973; MP PET 1991]
  A)
             \[3x-4y-19=0,\,\,3x-4y+31=0\] done clear
  B)
             \[4x+3y-19=0,\,\,4x+3y+31=0\] done clear
  C)
             \[4x+3y+19=0,\,\,4x+3y-31=0\] done clear
  D)
             \[3x-4y+19=0,3x-4y+31=0\] done clear
  View Solution play_arrow

• question_answer14)
  The equations of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}=36\]which are inclined at an angle of \[{{45}^{o}}\]to the x-axis are
  A)
             \[x+y=\pm \sqrt{6}\]              done clear
  B)
             \[x=y\pm 3\sqrt{2}\] done clear
  C)
             \[y=x\pm 6\sqrt{2}\]               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer15)
  A circle is given by \[{{x}^{2}}+{{y}^{2}}-6x+8y-11=0\]and there are two points (0, 0) and (1, 8). These points lie
  A)
             Both inside the circle done clear
  B)
             One outside and one inside the circle done clear
  C)
             Both outside the circle done clear
  D)
             One on and other inside the circle done clear
  View Solution play_arrow

• question_answer16)
  The length of tangent from the point (5, 1) to the circle \[{{x}^{2}}+{{y}^{2}}+6x-4y-3=0\], is                       [MNR 1981]
  A)
             81   done clear
  B)
             29 done clear
  C)
             7     done clear
  D)
             21 done clear
  View Solution play_arrow

• question_answer17)
  The equation of the normal to the circle \[{{x}^{2}}+{{y}^{2}}=9\]at the point \[\left( \frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)\]is
  A)
             \[x+y=0\]                                 done clear
  B)
             \[x-y=\frac{\sqrt{2}}{3}\] done clear
  C)
             \[x-y=0\]                                   done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer18)
  The equations of tangents to the circle \[{{x}^{2}}+{{y}^{2}}-22x-4y+25=0\] which are perpendicular to the line \[5x+12y+8=0\]are
  A)
             \[12x-5y+8=0\], \[12x-5y=252\] done clear
  B)
             \[12x-5y=0,\,\,12x-5y=252\] done clear
  C)
             \[12x-5y-8=0,\,12x-5y+252=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer19)
  The line \[x\cos \alpha +y\sin \alpha =p\]will be a tangent to the circle \[{{x}^{2}}+{{y}^{2}}-2ax\cos \alpha -2ay\sin \alpha =0\], if \[p=\]
  A)
             0 or a                                         done clear
  B)
             0 done clear
  C)
             \[2a\]                                          done clear
  D)
             \[0\]or \[2a\] done clear
  View Solution play_arrow

• question_answer20)
  If the line \[lx+my+n=0\]be a tangent to the circle \[{{(x-h)}^{2}}+{{(y-k)}^{2}}={{a}^{2}},\]then
  A)
             \[hl+km+n={{a}^{2}}({{l}^{2}}+{{m}^{2}})\] done clear
  B)
             \[{{(hl+km+n)}^{2}}=a({{l}^{2}}+{{m}^{2}})\] done clear
  C)
             \[{{(hl+km+n)}^{2}}={{a}^{2}}({{l}^{2}}+{{m}^{2}})\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer21)
  The line \[(x-a)\cos \alpha +(y-b)\]\[\sin \alpha =r\]will be a tangent to the circle \[{{(x-a)}^{2}}+{{(y-b)}^{2}}={{r}^{2}}\]
  A)
             If \[\alpha ={{30}^{o}}\]     done clear
  B)
             If \[\alpha ={{60}^{o}}\] done clear
  C)
             For all values of \[\alpha \]      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer22)
  The equations of the tangents drawn from the origin to the circle \[{{x}^{2}}+{{y}^{2}}-2rx-2hy+{{h}^{2}}=0\]are [Roorkee 1989; IIT 1988; RPET 1996]
  A)
             \[x=0,y=0\]                              done clear
  B)
             \[({{h}^{2}}-{{r}^{2}})x-2rhy=0,x=0\]                            done clear
  C)
             \[y=0,x=4\]                              done clear
  D)
             \[({{h}^{2}}-{{r}^{2}})x+2rhy=0,x=0\] done clear
  View Solution play_arrow

• question_answer23)
  An infinite number of tangents can be drawn from (1, 2) to the circle \[{{x}^{2}}+{{y}^{2}}-2x-4y+\lambda =0\], then \[\lambda =\] [MP PET 1989]
  A)
             ? 20                                           done clear
  B)
             0 done clear
  C)
             5     done clear
  D)
             Cannot be determined done clear
  View Solution play_arrow

• question_answer24)
  If the line \[lx+my=1\]be a tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], then the locus of the point (l, m) is [MNR 1978; RPET 1997]
  A)
             A straight line                            done clear
  B)
             A Circle done clear
  C)
             A parabola                                done clear
  D)
             An ellipse done clear
  View Solution play_arrow

• question_answer25)
  The equations of the tangents drawn from the point (0, 1) to the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y=0\]are               [Roorkee 1979]
  A)
             \[2x-y+1=0,\,\,x+2y-2=0\] done clear
  B)
             \[2x-y+1=0,\,\,x+2y+2=0\] done clear
  C)
             \[2x-y-1=0,\,\,x+2y-2=0\] done clear
  D)
             \[2x-y-1=0,\,\,x+2y+2=0\] done clear
  View Solution play_arrow

• question_answer26)
  The equations of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]parallel to the line \[\sqrt{3}x+y+3=0\]are
  A)
             \[\sqrt{3}x+y\pm 2a=0\]        done clear
  B)
             \[\sqrt{3}x+y\pm a=0\] done clear
  C)
             \[\sqrt{3}x+y\pm 4a=0\]        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer27)
  The angle between the tangents to the circle \[{{x}^{2}}+{{y}^{2}}=169\]at the points (5, 12) and (12, ?5), is
  A)
             \[{{30}^{o}}\]                       done clear
  B)
             \[{{45}^{o}}\] done clear
  C)
             \[{{60}^{o}}\]                       done clear
  D)
             \[{{90}^{o}}\] done clear
  View Solution play_arrow

• question_answer28)
  If the line \[x=k\]touches the circle \[{{x}^{2}}+{{y}^{2}}=9\], then the value of k is
  A)
             2 but not - 2                              done clear
  B)
             - 2 but not 2 done clear
  C)
             3     done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer29)
  If the line y \[\cos \alpha =x\sin \alpha +a\cos \alpha \]be a tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], then
  A)
             \[{{\sin }^{2}}\alpha =1\]    done clear
  B)
             \[{{\cos }^{2}}\alpha =1\] done clear
  C)
             \[{{\sin }^{2}}\alpha ={{a}^{2}}\]                                     done clear
  D)
             \[{{\cos }^{2}}\alpha ={{a}^{2}}\] done clear
  View Solution play_arrow

• question_answer30)
  Circle \[{{x}^{2}}+{{y}^{2}}-4x-8y-5=0\]will intersect the line \[3x-4y=m\] in two distinct points, if
  A)
             \[-10<m<5\]                            done clear
  B)
             \[9<m<20\] done clear
  C)
             \[-35<m<15\]                          done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer31)
  The two tangents to a circle from an external point are always                                        [MP PET 1986]
  A)
             Equal                                         done clear
  B)
             Perpendicular to each other done clear
  C)
             Parallel to each other               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer32)
  The area of the triangle formed by the tangents from the points (h, k) to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]and the line joining their points of contact is                                                   [MNR 1980]
  A)
             \[a\text{ }\frac{{{({{h}^{2}}+{{k}^{2}}-{{a}^{2}})}^{3/2}}}{{{h}^{2}}+{{k}^{2}}}\]            done clear
  B)
             \[a\text{ }\frac{{{({{h}^{2}}+{{k}^{2}}-{{a}^{2}})}^{1/2}}}{{{h}^{2}}+{{k}^{2}}}\] done clear
  C)
             \[\frac{{{({{h}^{2}}+{{k}^{2}}-{{a}^{2}})}^{3/2}}}{{{h}^{2}}+{{k}^{2}}}\]          done clear
  D)
             \[\frac{{{({{h}^{2}}+{{k}^{2}}-{{a}^{2}})}^{1/2}}}{{{h}^{2}}+{{k}^{2}}}\] done clear
  View Solution play_arrow

• question_answer33)
  If the equation of one tangent to the circle with centre at (2, ?1) from the origin is \[3x+y=0\], then the equation of the other tangent through the origin is
  A)
             \[3x-y=0\]                                 done clear
  B)
             \[x+3y=0\] done clear
  C)
             \[x-3y=0\]                                 done clear
  D)
             \[x+2y=0\] done clear
  View Solution play_arrow

• question_answer34)
  The equations of the normals to the circle \[{{x}^{2}}+{{y}^{2}}-8x-2y+12=0\]at the points whose ordinate is  ?1, will be
  A)
             \[2x-y-7=0,\,2x+y-9=0\]       done clear
  B)
             \[2x+y+7=0,\,2x+y+9=0\] done clear
  C)
             \[2x+y-7=0,\,\,2x+y+9=0\] done clear
  D)
             \[2x-y+7=0,\,2x-y+9=0\] done clear
  View Solution play_arrow

• question_answer35)
   If the ratio of the lengths of tangents drawn from the point \[(f,g)\]to the given circle \[{{x}^{2}}+{{y}^{2}}=6\]and \[{{x}^{2}}+{{y}^{2}}+3x+3y=0\]be 2 : 1, then
  A)
             \[{{f}^{2}}+{{g}^{2}}+2g+2f+2=0\]                             done clear
  B)
             \[{{f}^{2}}+{{g}^{2}}+4g+4f+4=0\] done clear
  C)
             \[{{f}^{2}}+{{g}^{2}}+4g+4f+2=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer36)
  If \[{{c}^{2}}>{{a}^{2}}(1+{{m}^{2}}),\]then the line \[y=mx+c\]will intersect the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]
  A)
             At one point                              done clear
  B)
             At two distinct points done clear
  C)
             At no point                                done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer37)
  The straight line \[x-y-3=0\]touches the circle \[{{x}^{2}}+{{y}^{2}}-4x+6y+11=0\]at the point whose co-ordinates are  [MP PET  1993]
  A)
             \[(1,-2)\]                                     done clear
  B)
             \[(1,\,2)\] done clear
  C)
             \[(-1,\,2)\]                                   done clear
  D)
             \[(-1,-2)\] done clear
  View Solution play_arrow

• question_answer38)
  The line \[y=mx+c\]will be a normal to the circle with radius r  and centre at (a, b), if
  A)
             \[a=mb+c\]                              done clear
  B)
             \[b=ma+c\] done clear
  C)
             \[r=ma-b+c\]                            done clear
  D)
             \[r=ma-b\] done clear
  View Solution play_arrow

• question_answer39)
  The point at which the normal to the circle \[{{x}^{2}}+{{y}^{2}}+4x+6y-39=0\]at the point (2, 3) will meet the circle again, is
  A)
             (6, -9)                                        done clear
  B)
             (6, 9) done clear
  C)
             (-6, -9)                                       done clear
  D)
             (-6, 9) done clear
  View Solution play_arrow

• question_answer40)
  The equation of the normal to the circle \[{{x}^{2}}+{{y}^{2}}-2x=0\]parallel to the line \[x+2y=3\]is
  A)
             \[2x+y-1=0\]                           done clear
  B)
             \[2x+y+1=0\] done clear
  C)
             \[x+2y-1=0\]                           done clear
  D)
             \[x+2y+1=0\] done clear
  View Solution play_arrow

• question_answer41)
  The equation of the tangent at the point \[\left( \frac{a{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}b}{{{a}^{2}}+{{b}^{2}}} \right)\] of the circle \[{{x}^{2}}+{{y}^{2}}=\frac{{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]is
  A)
             \[\frac{x}{a}+\frac{y}{b}=1\]       done clear
  B)
             \[\frac{x}{a}+\frac{y}{b}+1=0\] done clear
  C)
             \[\frac{x}{a}-\frac{y}{b}=1\] done clear
  D)
             \[\frac{x}{a}-\frac{y}{b}+1=0\] done clear
  View Solution play_arrow

• question_answer42)
  If a line passing through origin touches the circle \[{{(x-4)}^{2}}+{{(y+5)}^{2}}=25\], then its slope should be
  A)
             \[\pm \frac{3}{4}\]                   done clear
  B)
             0 done clear
  C)
             \[\pm \,3\]                                  done clear
  D)
             \[\pm \,1\] done clear
  View Solution play_arrow

• question_answer43)
  Two tangents drawn from the origin to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]will be perpendicular to each other, if                                  
  A)
             \[{{g}^{2}}+{{f}^{2}}=2c\]    done clear
  B)
             \[g=f={{c}^{2}}\] done clear
  C)
             \[g+f=c\]                                   done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer44)
  Length of the tangent drawn from any point on the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+{{c}_{1}}=0\] to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] is [Kerala (Engg.) 2002]
  A)
             \[\sqrt{{{c}_{1}}-c}\]              done clear
  B)
             \[\sqrt{c-{{c}_{1}}}\] done clear
  C)
             \[\sqrt{{{c}_{1}}+c}\]            done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer45)
  The equations of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}=13\]at the points whose abscissa is 2, are
  A)
             \[2x+3y=13,\,2x-3y=13\]     done clear
  B)
             \[3x+2y=13,\,2x-3y=13\] done clear
  C)
             \[2x+3y=13,\,\,3x-2y=13\]   done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer46)
  The equation of director circle of the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}},\]is  [BIT Ranchi 1990]
  A)
             \[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\]                            done clear
  B)
             \[{{x}^{2}}+{{y}^{2}}=\sqrt{2}{{a}^{2}}\] done clear
  C)
             \[{{x}^{2}}+{{y}^{2}}-2{{a}^{2}}=0\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer47)
  If O is the origin and OP, OQ  are tangents to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\], the circumcentre of the triangle \[OPQ\]is
  A)
             \[(-g,\,-f)\]                                   done clear
  B)
             \[(g,f)\] done clear
  C)
             \[(-f,-g)\]                                     done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer48)
  The equation of circle which touches the axes of coordinates and the line \[\frac{x}{3}+\frac{y}{4}=1\]and whose centre lies in the first quadrant is \[{{x}^{2}}+{{y}^{2}}-2cx-2cy+{{c}^{2}}=0\], where c is  [BIT Ranchi 1986; Kurukshetra CEE 1996]
  A)
             1     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             6 done clear
  View Solution play_arrow

• question_answer49)
  The number of tangents which can be drawn from the point (?1,2) to the circle \[{{x}^{2}}+{{y}^{2}}+2x-4y+4=0\] is [BIT Ranchi 1991]
  A)
             1     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             0 done clear
  View Solution play_arrow

• question_answer50)
  The number of tangents that can be drawn from (0, 0) to the circle \[{{x}^{2}}+{{y}^{2}}+2x+6y-15=0\]is                               [MP PET 1992]
  A)
             None                                         done clear
  B)
             One done clear
  C)
             Two done clear
  D)
             Infinite done clear
  View Solution play_arrow

• question_answer51)
  At which point on y-axis the line \[x=0\]is a tangent to circle \[{{x}^{2}}+{{y}^{2}}-2x-6y+9=0\]                                  [RPET 1984]
  A)
             (0, 1)                                          done clear
  B)
             (0, 2) done clear
  C)
             (0, 3)                                          done clear
  D)
             (0, 4) done clear
  View Solution play_arrow

• question_answer52)
  The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\]and\[{{x}^{2}}+{{y}^{2}}+6x+18y+26=0\]is  [MP PET 1995]
  A)
             1     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer53)
  If the straight line \[y=mx+c\]touches the circle \[{{x}^{2}}+{{y}^{2}}-4y=0\], then the value of c will be      [RPET 1988]
  A)
             \[1+\sqrt{1+{{m}^{2}}}\]  done clear
  B)
             \[1-\sqrt{{{m}^{2}}+1}\] done clear
  C)
             \[2(1+\sqrt{1+{{m}^{2}}})\]     done clear
  D)
             \[2+\sqrt{1+{{m}^{2}}}\] done clear
  View Solution play_arrow

• question_answer54)
  The area of triangle formed by the tangent, normal drawn at \[(1,\sqrt{3})\]to the circle \[{{x}^{2}}+{{y}^{2}}=4\]and positive x-axis, is [IIT 1989; RPET 1997, 99; Kurukshetra CEE 1998]
  A)
             \[2\sqrt{3}\]                              done clear
  B)
             \[\sqrt{3}\] done clear
  C)
             \[4\sqrt{3}\]                              done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer55)
  Line \[y=x+a\sqrt{2}\] is a tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]at    [RPET 1991; MP PET 1999]
  A)
             \[\left( \frac{a}{\sqrt{2}},\frac{a}{\sqrt{2}} \right)\]                done clear
  B)
             \[\left( -\frac{a}{\sqrt{2}},-\frac{a}{\sqrt{2}} \right)\] done clear
  C)
             \[\left( \frac{a}{\sqrt{2}},-\frac{a}{\sqrt{2}} \right)\]               done clear
  D)
             \[\left( -\frac{a}{\sqrt{2}},\frac{a}{\sqrt{2}} \right)\] done clear
  View Solution play_arrow

• question_answer56)
  The point of contact of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}=5\]at the point (1, ?2) which touches the circle \[{{x}^{2}}+{{y}^{2}}-8x+6y+20=0\], is                                                                [Roorkee 1989]
  A)
             (2, -1)                                        done clear
  B)
             (3, -1) done clear
  C)
             (4, -1)                                        done clear
  D)
             (5, -1) done clear
  View Solution play_arrow

• question_answer57)
  The normal to the circle \[{{x}^{2}}+{{y}^{2}}-3x-6y-10=0\]at the point (?3, 4), is                                           [RPET 1986, 89]
  A)
             \[2x+9y-30=0\]                       done clear
  B)
             \[9x-2y+35=0\] done clear
  C)
             \[2x-9y+30=0\]                       done clear
  D)
             \[2x-9y-30=0\] done clear
  View Solution play_arrow

• question_answer58)
  A tangent to the circle \[{{x}^{2}}+{{y}^{2}}=5\]at the point (1,?2)..... the circle \[{{x}^{2}}+{{y}^{2}}-8x+6y+20=0\]                    [IIT 1975]
  A)
             Touches                                    done clear
  B)
             Cuts at real points done clear
  C)
             Cuts at imaginary points          done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer59)
  The line \[y=x+c\]will intersect the circle \[{{x}^{2}}+{{y}^{2}}=1\]in two coincident points, if
  A)
             \[c=\sqrt{2}\]                            done clear
  B)
             \[c=-\sqrt{2}\] done clear
  C)
             \[c=\pm \sqrt{2}\]                    done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer60)
  Which of the following lines is a tangent to the circle \[{{x}^{2}}+{{y}^{2}}=25\]for all values of m
  A)
             \[y=mx+25\sqrt{1+{{m}^{2}}}\]                                         done clear
  B)
             \[y=mx+5\sqrt{1+{{m}^{2}}}\] done clear
  C)
             \[y=mx+25\sqrt{1-{{m}^{2}}}\]                                           done clear
  D)
             \[y=mx+5\sqrt{1-{{m}^{2}}}\] done clear
  View Solution play_arrow

• question_answer61)
  Square of the length of the tangent drawn from the point \[(\alpha ,\beta )\]to the circle \[a{{x}^{2}}+a{{y}^{2}}={{r}^{2}}\]is
  A)
             \[a{{\alpha }^{2}}+a{{\beta }^{2}}-{{r}^{2}}\]            done clear
  B)
             \[{{\alpha }^{2}}+{{\beta }^{2}}-\frac{{{r}^{2}}}{a}\] done clear
  C)
             \[{{\alpha }^{2}}+{{\beta }^{2}}+\frac{{{r}^{2}}}{a}\]           done clear
  D)
             \[{{\alpha }^{2}}+{{\beta }^{2}}-{{r}^{2}}\] done clear
  View Solution play_arrow

• question_answer62)
  The points of contact of the circle \[{{x}^{2}}+{{y}^{2}}+2x+2y+1=0\]and the co-ordinate axes are
  A)
             \[(1,\,0),(0,\,1)\]                         done clear
  B)
             \[(-1,\,0),(0,\,1)\] done clear
  C)
             \[(-1,\,0),(0,\,-1)\]                      done clear
  D)
             \[(1,\,\,0),(0,\,-1)\] done clear
  View Solution play_arrow

• question_answer63)
  x\[y-x+3=0\]is the equation of normal at \[\left( 3+\frac{3}{\sqrt{2}},\frac{3}{\sqrt{2}} \right)\] to which of the following circles                        [Roorkee 1990]
  A)
             \[{{\left( x-3-\frac{3}{\sqrt{2}} \right)}^{2}}+{{\left( y-\frac{\sqrt{3}}{2} \right)}^{2}}=9\] done clear
  B)
             \[{{\left( x-3-\frac{3}{\sqrt{2}} \right)}^{2}}+{{y}^{2}}=6\] done clear
  C)
             \[{{(x-3)}^{2}}+{{y}^{2}}=9\] done clear
  D)
             \[{{(x-3)}^{2}}+{{(y-3)}^{2}}=9\] done clear
  View Solution play_arrow

• question_answer64)
  If the straight line \[y=mx+c\]touches the circle \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\]at the point (2, 3), then c =
  A)
             - 3   done clear
  B)
             4 done clear
  C)
             5     done clear
  D)
             ? 2 done clear
  View Solution play_arrow

• question_answer65)
  Length  of the tangent from \[({{x}_{1}},{{y}_{1}})\]to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] is                                                [EAMCET 1980]
  A)
             \[{{(x_{1}^{2}+y_{1}^{2}+2g{{x}_{1}}+2f{{y}_{1}}+c)}^{1/2}}\] done clear
  B)
             \[{{(x_{1}^{2}+y_{1}^{2})}^{1/2}}\] done clear
  C)
             \[{{[{{({{x}_{1}}+g)}^{2}}+{{({{y}_{1}}+f)}^{2}}]}^{1/2}}\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer66)
  The point (0.1, 3.1) with respect to the circle \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\], is                                        [MNR 1980]
  A)
             At the centre of the circle done clear
  B)
             Inside the circle but not at the centre done clear
  C)
             On the circle done clear
  D)
             Outside the circle done clear
  View Solution play_arrow

• question_answer67)
  The points of intersection of the line \[4x-3y-10=0\] and the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y-20=0\] are               [IIT 1983]
  A)
             \[(-2,-6),(4,2)\]                          done clear
  B)
             \[(2,\,6),(-4,-2)\] done clear
  C)
             \[(-2,\,6),(-4,\,2)\]                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer68)
  The equation of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\] at \[(a,b)\]is \[ax+by-\lambda =0\], where \[\lambda \]is
  A)
             \[{{a}^{2}}\]                          done clear
  B)
             \[{{b}^{2}}\] done clear
  C)
             \[{{r}^{2}}\]                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer69)
  If the centre of a circle is (?6, 8) and it passes through the origin, then equation to its tangent at the origin, is [MNR 1976]
  A)
             \[2y=x\]                                     done clear
  B)
             \[4y=3x\] done clear
  C)
             \[3y=4x\]                                  done clear
  D)
             \[3x+4y=0\] done clear
  View Solution play_arrow

• question_answer70)
  The line \[y=mx+c\]intersects the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\]at two real distinct points, if
  A)
             \[-r\sqrt{1+{{m}^{2}}}<c\le 0\]                                            done clear
  B)
             \[0\le c<r\sqrt{1+{{m}^{2}}}\] done clear
  C)
             (a) and (b) both                        done clear
  D)
             \[-c\sqrt{1-{{m}^{2}}}<r\] done clear
  View Solution play_arrow

• question_answer71)
  The locus of the point of intersection of the tangents at the extremities of a chord of the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]which  touches the circle \[{{x}^{2}}+{{y}^{2}}=2ax\]is
  A)
             \[{{y}^{2}}=a\text{ }(a-2x)\]      done clear
  B)
             \[{{x}^{2}}=a\text{ }(a-2y)\] done clear
  C)
             \[{{x}^{2}}+{{y}^{2}}={{(y-a)}^{2}}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer72)
  The equation of pair of tangents to the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y+3=0\]from \[(6,-5)\], is               [AMU 1980]
  A)
             \[7{{x}^{2}}+23{{y}^{2}}+30xy+66x+50y-73=0\] done clear
  B)
             \[7{{x}^{2}}+23{{y}^{2}}+30xy-66x-50y-73=0\] done clear
  C)
             \[7{{x}^{2}}+23{{y}^{2}}-30xy-66x-50y+73=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer73)
  . If OA and OB are the tangents from the origin to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]and C is the centre of the circle, the area of the quadrilateral \[OACB\]is
  A)
             \[\frac{1}{2}\sqrt{c({{g}^{2}}+{{f}^{2}}-c)}\]                 done clear
  B)
             \[\sqrt{c({{g}^{2}}+{{f}^{2}}-c)}\] done clear
  C)
             \[c\sqrt{{{g}^{2}}+{{f}^{2}}-c}\]                                       done clear
  D)
             \[\frac{\sqrt{{{g}^{2}}+{{f}^{2}}-c}}{c}\] done clear
  View Solution play_arrow

• question_answer74)
  The values of constant term in the equation of circle passing through (1, 2) and (3, 4) and touching the line \[3x+y-3=0\], is
  A)
             7 and 12                                   done clear
  B)
             Only 7 done clear
  C)
             Only 12                                     done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer75)
  The gradient of the tangent line at the point \[(a\cos \alpha ,a\sin \alpha )\]to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], is
  A)
             \[\tan \alpha \]                           done clear
  B)
             \[\tan (\pi -\alpha )\] done clear
  C)
             \[\cot \alpha \]                            done clear
  D)
             \[-\cot \alpha \] done clear
  View Solution play_arrow

• question_answer76)
  The two circles which passes through \[(0,a)\]and \[(0,-a)\]and touch the line \[y=mx+c\] will intersect each other at right angle, if
  A)
             \[{{a}^{2}}={{c}^{2}}(2m+1)\]                                        done clear
  B)
             \[{{a}^{2}}={{c}^{2}}(2+{{m}^{2}})\] done clear
  C)
             \[{{c}^{2}}={{a}^{2}}(2+{{m}^{2}})\]                        done clear
  D)
             \[{{c}^{2}}={{a}^{2}}(2m+1)\] done clear
  View Solution play_arrow

• question_answer77)
  The equation of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\] which make equal intercepts on the positive coordinate axes is given by
  A)
             \[x+y+2\sqrt{2}=0\]              done clear
  B)
             \[x+y=2\sqrt{2}\] done clear
  C)
             \[x+y=2\]                                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer78)
  The angle between the tangents from \[(\alpha ,\beta )\]to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], is
  A)
             \[{{\tan }^{-1}}\left( \frac{a}{\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}-{{a}^{2}}}} \right)\]   done clear
  B)
             \[{{\tan }^{-1}}\left( \frac{\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}-{{a}^{2}}}}{a} \right)\] done clear
  C)
             \[2{{\tan }^{-1}}\left( \frac{a}{\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}-{{a}^{2}}}} \right)\]                done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer79)
  The equation of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}-2x-4y-4=0\] which is perpendicular to \[3x-4y-1=0\], is
  A)
             \[4x+3y-5=0\]                         done clear
  B)
             \[4x+3y+25=0\] done clear
  C)
             \[4x-3y+5=0\]                         done clear
  D)
             \[4x+3y-25=0\] done clear
  View Solution play_arrow

• question_answer80)
  The equation of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]which makes a triangle of area \[{{a}^{2}}\] with the co-ordinate axes, is
  A)
             \[x\pm y=a\sqrt{2}\]                done clear
  B)
             \[x\pm y=\pm a\sqrt{2}\] done clear
  C)
             \[x\pm y=2a\]                           done clear
  D)
             \[x+y=\pm 2a\] done clear
  View Solution play_arrow

• question_answer81)
  If the line \[3x-4y=\lambda \]touches the circle \[{{x}^{2}}+{{y}^{2}}-4x-8y-5=0\], then \[\lambda \]is equal to [Roorkee 1972; Kurukshetra CEE 1996]
  A)
             - 35, -15                                    done clear
  B)
             - 35, 15 done clear
  C)
             35, 15                                        done clear
  D)
             35, -15 done clear
  View Solution play_arrow

• question_answer82)
   If a circle passes through the points of intersection of the coordinate axis with the lines \[\lambda x-y+1=0\]and \[x-2y+3=0\], then the value of \[\lambda \]is                                        [IIT 1991]
  A)
             1     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer83)
  Tangents drawn from origin to the circle \[{{x}^{2}}+{{y}^{2}}-2ax-2by+{{b}^{2}}=0\]are perpendicular to each other, if   [MP PET 1995]
  A)
             \[a-b=1\]                                   done clear
  B)
             \[a+b=1\] done clear
  C)
             \[{{a}^{2}}={{b}^{2}}\]  done clear
  D)
             \[{{a}^{2}}+{{b}^{2}}=1\] done clear
  View Solution play_arrow

• question_answer84)
  The line \[lx+my+n=0\]is normal to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\], if                              [MP PET 1995]
  A)
             \[lg+mf-n=0\]                          done clear
  B)
             \[lg+mf+n=0\] done clear
  C)
             \[lg=mf-n=0\]                          done clear
  D)
             \[lg-mf+n=0\] done clear
  View Solution play_arrow

• question_answer85)
  Given the circles \[{{x}^{2}}+{{y}^{2}}-4x-5=0\]and\[{{x}^{2}}+{{y}^{2}}+6x-2y+6=0\]. Let P be a point \[(\alpha ,\beta )\]such that the tangents from P to both the circles are equal, then
  A)
             \[2\alpha +10\beta +11=0\] done clear
  B)
             \[2\alpha -10\beta +11=0\] done clear
  C)
             \[10\alpha -2\beta +11=0\]   done clear
  D)
             \[10\alpha +2\beta +11=0\] done clear
  View Solution play_arrow

• question_answer86)
  The number of common tangents to two circles \[{{x}^{2}}+{{y}^{2}}=4\]and \[{{x}^{2}}-{{y}^{2}}-8x+12=0\]is            [EAMCET  1990]
  A)
             1     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer87)
  If \[2x-4y=9\]and \[6x-12y+7=0\]are the tangents of same circle, then its radius will be                                           [Roorkee 1995]
  A)
             \[\frac{\sqrt{3}}{5}\]               done clear
  B)
             \[\frac{17}{6\sqrt{5}}\] done clear
  C)
             \[\frac{2\sqrt{5}}{3}\]             done clear
  D)
             \[\frac{17}{3\sqrt{5}}\] done clear
  View Solution play_arrow

• question_answer88)
  The tangent at P, any point on the circle \[{{x}^{2}}+{{y}^{2}}=4\], meets the coordinate axes in A and B, then
  A)
             Length of AB is constant done clear
  B)
             PA and PB are always equal done clear
  C)
             The locus of the midpoint of AB is \[{{x}^{2}}+{{y}^{2}}={{x}^{2}}{{y}^{2}}\]             done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer89)
  The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}-x=0,\,{{x}^{2}}+{{y}^{2}}+x=0\]is                         [EAMCET 1994]
  A)
             2     done clear
  B)
             1 done clear
  C)
             4     done clear
  D)
             3 done clear
  View Solution play_arrow

• question_answer90)
  The equation of tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] parallel to\[y=mx+c\]is                                                [RPET 2001]
  A)
             \[y=mx\pm \sqrt{1+{{m}^{2}}}\]                                         done clear
  B)
             \[y=mx\pm a\sqrt{1+{{m}^{2}}}\] done clear
  C)
             \[x=my\pm a\sqrt{1+{{m}^{2}}}\]                                       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer91)
  If the circle \[{{(x-h)}^{2}}+{{(y-k)}^{2}}={{r}^{2}}\] touches the curve \[y={{x}^{2}}+1\]at a point (1, 2), then the possible locations of the points (h, k) are given by                                           [AMU 2000]
  A)
             \[hk=5/2\]                                 done clear
  B)
             \[h+2k=5\] done clear
  C)
             \[{{h}^{2}}-4{{k}^{2}}=5\]    done clear
  D)
             \[{{k}^{2}}={{h}^{2}}+1\] done clear
  View Solution play_arrow

• question_answer92)
  The line \[ax+by+c=0\] is a normal to the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\]. The portion of the line \[ax+by+c=0\] intercepted by this circle is of length 
  A)
             r      done clear
  B)
             \[{{r}^{2}}\] done clear
  C)
             2r    done clear
  D)
             \[\sqrt{r}\] done clear
  View Solution play_arrow

• question_answer93)
  \[x=7\] touches the circle \[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\], then the coordinates of the point of contact are           [MP PET 1996]
  A)
             (7, 3)                                          done clear
  B)
             (7, 4) done clear
  C)
             (7, 8)                                          done clear
  D)
             (7, 2) done clear
  View Solution play_arrow

• question_answer94)
  If \[a>2b>0\]then the positive value of m for which \[y=mx-b\sqrt{1+{{m}^{2}}}\]is a common tangent to \[{{x}^{2}}+{{y}^{2}}={{b}^{2}}\]and \[{{(x-a)}^{2}}+{{y}^{2}}={{b}^{2}}\], is            [IIT Screening 2002]
  A)
             \[\frac{2b}{\sqrt{{{a}^{2}}-4{{b}^{2}}}}\]                      done clear
  B)
             \[\frac{\sqrt{{{a}^{2}}-4{{b}^{2}}}}{2b}\] done clear
  C)
             \[\frac{2b}{a-2b}\]                   done clear
  D)
             \[\frac{b}{a-2b}\] done clear
  View Solution play_arrow

• question_answer95)
  The circles \[{{x}^{2}}+{{y}^{2}}=9\]and \[{{x}^{2}}+{{y}^{2}}-12y+27=0\] touch each other. The equation of their common tangent is  [MP PET 1998]
  A)
             \[4y=9\]                                    done clear
  B)
             \[y=3\] done clear
  C)
             \[y=-3\]                                     done clear
  D)
             \[x=3\] done clear
  View Solution play_arrow

• question_answer96)
  If a circle, whose centre is (?1, 1) touches the straight line \[x+2y+12=0\], then the coordinates of the point of contact are [MP PET 1998]
  A)
             \[\left( \frac{-7}{2},-4 \right)\] done clear
  B)
             \[\left( \frac{-18}{5},\frac{-21}{5} \right)\] done clear
  C)
             (2,-7)                                         done clear
  D)
             (-2, -5) done clear
  View Solution play_arrow

• question_answer97)
  If the tangent at a point \[P(x,y)\] of a curve is perpendicular to the line that joins origin with the point P, then the curve is [MP PET 1998]
  A)
             Circle                                         done clear
  B)
             Parabola done clear
  C)
             Ellipse                                        done clear
  D)
             Straight line done clear
  View Solution play_arrow

• question_answer98)
  The slope of the tangent at the point \[(h,h)\]of the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]is
  A)
  0     done clear
  B)
  1 done clear
  C)
  -1   done clear
  D)
  Depends on h done clear
  View Solution play_arrow

• question_answer99)
  If the straight line \[4x+3y+\lambda =0\]touches the circle \[2({{x}^{2}}+{{y}^{2}})=5\], then \[\lambda \]is
  A)
             \[\frac{5\sqrt{5}}{2}\]             done clear
  B)
             \[5\sqrt{2}\] done clear
  C)
             \[\frac{5\sqrt{5}}{4}\]             done clear
  D)
             \[\frac{5\sqrt{10}}{2}\] done clear
  View Solution play_arrow

• question_answer100)
  The gradient of the normal at the point (-2, -3) on the circle \[{{x}^{2}}+{{y}^{2}}+2x+4y+3=0\]is
  A)
             1     done clear
  B)
             -1 done clear
  C)
             \[\frac{3}{2}\]                           done clear
  D)
             \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer101)
  Equation of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]which is perpendicular to the straight line \[y=mx+c\]is 
  A)
             \[y=-\frac{x}{m}\pm a\sqrt{1+{{m}^{2}}}\]                       done clear
  B)
             \[x+my=\pm \text{ }a\text{ }\sqrt{1+{{m}^{2}}}\] done clear
  C)
             \[x+my=\pm a\sqrt{1+{{(1/m)}^{2}}}\]                              done clear
  D)
             \[x-my=\pm a\sqrt{1+{{m}^{2}}}\] done clear
  View Solution play_arrow

• question_answer102)
  A circle with centre (a, b) passes through the origin. The equation of the tangent to the circle at the origin is [RPET 2000]
  A)
             \[ax-by=0\]                               done clear
  B)
             \[ax+by=0\] done clear
  C)
             \[bx-ay=0\]                               done clear
  D)
             \[bx+ay=0\] done clear
  View Solution play_arrow

• question_answer103)
  The two circles \[{{x}^{2}}+{{y}^{2}}-2x+6y+6=0\]and \[{{x}^{2}}+{{y}^{2}}-5x+6y+15=0\]touch each other. The equation of their common tangent is [DCE 1999]
  A)
             \[x=3\]                                       done clear
  B)
             \[y=6\] done clear
  C)
             \[7x-12y-21=0\]                      done clear
  D)
             \[7x+12y+21=0\] done clear
  View Solution play_arrow

• question_answer104)
  The length of the tangent from the point (4, 5)to the circle \[{{x}^{2}}+{{y}^{2}}+2x-6y=6\]is                                       [DCE 1999]
  A)
             \[\sqrt{13}\]                              done clear
  B)
             \[\sqrt{38}\] done clear
  C)
             \[2\sqrt{2}\]                              done clear
  D)
             \[2\sqrt{13}\] done clear
  View Solution play_arrow

• question_answer105)
  The equation to the tangents to the circle \[{{x}^{2}}+{{y}^{2}}=4\], which are parallel to \[x+2y+3=0\], are [MP PET 2003]
  A)
             \[x-2y=2\]                                 done clear
  B)
             \[x+2y=\pm \,2\sqrt{3}\] done clear
  C)
             \[x+2y=\pm \,2\sqrt{5}\]        done clear
  D)
             \[x-2y=\pm \,2\sqrt{5}\] done clear
  View Solution play_arrow

• question_answer106)
  The equation of normal to the circle \[2{{x}^{2}}+2{{y}^{2}}-2x-5y+3=0\]at (1, 1) is     [MP PET 2001]
  A)
             \[2x+y=3\]                               done clear
  B)
             \[x-2y=3\] done clear
  C)
             \[x+2y=3\]                               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer107)
   The square of the length of the tangent from      (3, ?4) on the circle \[{{x}^{2}}+{{y}^{2}}-4x-6y+3=0\]is [MP PET 2000]
  A)
             20   done clear
  B)
             30 done clear
  C)
             40   done clear
  D)
             50 done clear
  View Solution play_arrow

• question_answer108)
  The condition that the line \[x\cos \alpha +y\sin \alpha =p\] may touch the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] is                                             [AMU 1999]
  A)
             \[p=a\cos \alpha \]                   done clear
  B)
             \[p=a\tan \alpha \] done clear
  C)
             \[{{p}^{2}}={{a}^{2}}\]  done clear
  D)
             \[p\sin \alpha =a\] done clear
  View Solution play_arrow

• question_answer109)
  The line \[3x-2y=k\]meets the circle \[{{x}^{2}}+{{y}^{2}}=4{{r}^{2}}\]at only one point, if  \[{{k}^{2}}\]=                                           [Karnataka CET 2003]
  A)
             \[20{{r}^{2}}\]                      done clear
  B)
             \[52{{r}^{2}}\] done clear
  C)
             \[\frac{52}{9}{{r}^{2}}\]     done clear
  D)
             \[\frac{20}{9}{{r}^{2}}\] done clear
  View Solution play_arrow

• question_answer110)
   If \[5x-12y+10=0\]and \[12y-5x+16=0\]are two tangents to a circle, then the radius of the circle is      [EAMCET 2003]
  A)
             1     done clear
  B)
             2 done clear
  C)
             4     done clear
  D)
             6 done clear
  View Solution play_arrow

• question_answer111)
  The area of the triangle formed by the tangent at    (3, 4) to the circle \[{{x}^{2}}+{{y}^{2}}=25\]and the co-ordinate axes is  [Pb. CET 2004]
  A)
             \[\frac{24}{25}\]                      done clear
  B)
             0 done clear
  C)
             \[\frac{625}{24}\]                    done clear
  D)
             \[-\left( \frac{24}{25} \right)\] done clear
  View Solution play_arrow

• question_answer112)
  The value of c,  for which the line \[y=2x+c\]is a tangent to the circle \[{{x}^{2}}+{{y}^{2}}=16\], is [MP PET 2004; Karnataka CET 2005]
  A)
             \[-16\sqrt{5}\]                           done clear
  B)
             20 done clear
  C)
             \[4\sqrt{5}\]                              done clear
  D)
             \[16\sqrt{5}\] done clear
  View Solution play_arrow

• question_answer113)
  The equations of the tangents to circle \[5{{x}^{2}}+5{{y}^{2}}=1\], parallel to line \[3x+4y=1\] are                           [J & K 2005]
  A)
             \[3x+4y=\pm 2\sqrt{5}\]       done clear
  B)
             \[6x+8y=\pm \sqrt{5}\] done clear
  C)
           \[3x+4y=\pm \sqrt{5}\]      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer114)
  Consider the following statements : Assertion  : The circle \[{{x}^{2}}+{{y}^{2}}=1\]has exactly two tangents parallel to the x-axis Reason (R) : \[\frac{dy}{dx}=0\] on  the circle exactly at the point \[(0,\pm 1)\]. Of these statements                                     [SCRA 1996]
  A)
             Both A and R are true and R is the correct explanation of A done clear
  B)
             Both A and R are true but R is not the correct explanation of A done clear
  C)
             A is true but R is false done clear
  D)
             A is false but R is true done clear
  View Solution play_arrow

• question_answer115)
  If \[\frac{x}{\alpha }+\frac{y}{\beta }=1\] touches the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], then point \[(1/\alpha ,\,1/\beta )\]lies on a/an                                                               [Orissa JEE 2005]
  A)
             Straight line                               done clear
  B)
             Circle done clear
  C)
             Parabola                                    done clear
  D)
             Ellipse done clear
  View Solution play_arrow

• question_answer116)
  Give the number of common tangents to circle \[{{x}^{2}}+{{y}^{2}}+2x+8y-23=0\] and \[{{x}^{2}}+{{y}^{2}}-4x-10y+9=0\] [Orissa JEE 2005]
  A)
             1     done clear
  B)
             3 done clear
  C)
             2     done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer117)
  The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}=1\]and \[{{x}^{2}}+{{y}^{2}}-4x+3=0\] is            [DCE 2005]
  A)
             1     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer118)
  If line \[ax+by=0\] touches \[{{x}^{2}}+{{y}^{2}}+2x+4y=0\] and is a normal to the circle \[{{x}^{2}}+{{y}^{2}}-4x+2y-3=0\], then value of (a,b) will be [AMU 2005]
  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_answer119)
  If the equation of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}-2x+6y-6=0\] parallel to \[3x-4y+7=0\] is \[3x-4y+k=0\], then the values of k are [Kerala (Engg.) 2005]
  A)
             5, -35                                         done clear
  B)
             -5, 35 done clear
  C)
             7, -32                                         done clear
  D)
              -7, 32 done clear
  E)
             3, -13 done clear
  View Solution play_arrow

• question_answer120)
  The locus of a point which moves so that the ratio of the length of the tangents to the circles \[{{x}^{2}}+{{y}^{2}}+4x+3=0\] and \[{{x}^{2}}+{{y}^{2}}-6x+5=0\] is 2:3  is                                                               [Kerala (Engg.) 2005]
  A)
             \[5{{x}^{2}}+5{{y}^{2}}-60x+7=0\]                              done clear
  B)
             \[5{{x}^{2}}+5{{y}^{2}}+60x-7=0\] done clear
  C)
             \[5{{x}^{2}}+5{{y}^{2}}-60x-7=0\]                                done clear
  D)
             \[5{{x}^{2}}+5{{y}^{2}}+60x+7=0\] done clear
  E)
             \[5{{x}^{2}}+5{{y}^{2}}+60x+12=0\] done clear
  View Solution play_arrow