-
question_answer1)
A point on the curve \[\frac{{{x}^{2}}}{{{A}^{2}}}-\frac{{{y}^{2}}}{{{B}^{2}}}=1\] is [MP PET 1988]
A)
\[(A\cos \theta ,\ B\sin \theta )\] done
clear
B)
\[(A\sec \theta ,\ B\tan \theta )\] done
clear
C)
\[(A{{\cos }^{2}}\theta ,\ B{{\sin }^{2}}\theta )\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer2)
If the eccentricities of the hyperbolas \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and \[\frac{{{y}^{2}}}{{{b}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}}=1\] be e and \[{{e}_{1}}\], then \[\frac{1}{{{e}^{2}}}+\frac{1}{e_{1}^{2}}=\] [MNR 1984; MP PET 1995; DCE 2000]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer3)
If P is a point on the hyperbola \[16{{x}^{2}}-9{{y}^{2}}=144\] whose foci are \[{{S}_{1}}\] and \[{{S}_{2}}\], then \[P{{S}_{1}}\tilde{\ }P{{S}_{2}}=\]
A)
4 done
clear
B)
6 done
clear
C)
8 done
clear
D)
12 done
clear
View Solution play_arrow
-
question_answer4)
If the latus rectum of an hyperbola be 8 and eccentricity be \[3/\sqrt{5}\], then the equation of the hyperbola is
A)
\[4{{x}^{2}}-5{{y}^{2}}=100\] done
clear
B)
\[5{{x}^{2}}-4{{y}^{2}}=100\] done
clear
C)
\[4{{x}^{2}}+5{{y}^{2}}=100\] done
clear
D)
\[5{{x}^{2}}+4{{y}^{2}}=100\] done
clear
View Solution play_arrow
-
question_answer5)
The eccentricity of a hyperbola passing through the points (3, 0), \[(3\sqrt{2},\ 2)\] will be [MNR 1985; UPSEAT 2000]
A)
\[\sqrt{13}\] done
clear
B)
\[\frac{\sqrt{13}}{3}\] done
clear
C)
\[\frac{\sqrt{13}}{4}\] done
clear
D)
\[\frac{\sqrt{13}}{2}\] done
clear
View Solution play_arrow
-
question_answer6)
The one which does not represent a hyperbola is [MP PET 1992]
A)
\[xy=1\] done
clear
B)
\[{{x}^{2}}-{{y}^{2}}=5\] done
clear
C)
\[(x-1)(y-3)=3\] done
clear
D)
\[{{x}^{2}}-{{y}^{2}}=0\] done
clear
View Solution play_arrow
-
question_answer7)
The equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13, is
A)
\[25{{x}^{2}}-144{{y}^{2}}=900\] done
clear
B)
\[144{{x}^{2}}-25{{y}^{2}}=900\] done
clear
C)
\[144{{x}^{2}}+25{{y}^{2}}=900\] done
clear
D)
\[25{{x}^{2}}+144{{y}^{2}}=900\] done
clear
View Solution play_arrow
-
question_answer8)
The length of the transverse axis of a hyperbola is 7 and it passes through the point (5, ?2). The equation of the hyperbola is
A)
\[\frac{4}{49}{{x}^{2}}-\frac{196}{51}{{y}^{2}}=1\] done
clear
B)
\[\frac{49}{4}{{x}^{2}}-\frac{51}{196}{{y}^{2}}=1\] done
clear
C)
\[\frac{4}{49}{{x}^{2}}-\frac{51}{196}{{y}^{2}}=1\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer9)
If (4, 0) and (?4, 0) be the vertices and (6, 0) and (?6, 0) be the foci of a hyperbola, then its eccentricity is
A)
5/2 done
clear
B)
2 done
clear
C)
3/2 done
clear
D)
\[\sqrt{2}\] done
clear
View Solution play_arrow
-
question_answer10)
The eccentricity of the hyperbola \[{{x}^{2}}-{{y}^{2}}=25\] is [MP PET 1987]
A)
\[\sqrt{2}\] done
clear
B)
\[1/\sqrt{2}\] done
clear
C)
2 done
clear
D)
\[1+\sqrt{2}\] done
clear
View Solution play_arrow
-
question_answer11)
The equation of the transverse and conjugate axis of the hyperbola \[16{{x}^{2}}-{{y}^{2}}+64x+4y+44=0\] are
A)
\[x=2,\ y+2=0\] done
clear
B)
\[x=2,\ y=2\] done
clear
C)
\[y=2,\ x+2=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer12)
If the length of the transverse and conjugate axes of a hyperbola be 8 and 6 respectively, then the difference focal distances of any point of the hyperbola will be
A)
8 done
clear
B)
6 done
clear
C)
14 done
clear
D)
2 done
clear
View Solution play_arrow
-
question_answer13)
If \[(0,\ \pm 4)\] and \[(0,\ \pm 2)\] be the foci and vertices of a hyperbola, then its equation is
A)
\[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{12}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{12}-\frac{{{y}^{2}}}{4}=1\] done
clear
C)
\[\frac{{{y}^{2}}}{4}-\frac{{{x}^{2}}}{12}=1\] done
clear
D)
\[\frac{{{y}^{2}}}{12}-\frac{{{x}^{2}}}{4}=1\] done
clear
View Solution play_arrow
-
question_answer14)
The locus of the point of intersection of the lines \[bxt-ayt=ab\] and \[bx+ay=abt\] is
A)
A parabola done
clear
B)
An ellipse done
clear
C)
A hyperbola done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer15)
The locus of the point of intersection of the lines \[ax\sec \theta +by\tan \theta =a\] and \[ax\tan \theta +by\sec \theta =b\], where \[\theta \] is the parameter, is
A)
A straight line done
clear
B)
A circle done
clear
C)
An ellipse done
clear
D)
A hyperbola done
clear
View Solution play_arrow
-
question_answer16)
If the centre, vertex and focus of a hyperbola be (0, 0), (4, 0) and (6, 0) respectively, then the equation of the hyperbola is
A)
\[4{{x}^{2}}-5{{y}^{2}}=8\] done
clear
B)
\[4{{x}^{2}}-5{{y}^{2}}=80\] done
clear
C)
\[5{{x}^{2}}-4{{y}^{2}}=80\] done
clear
D)
\[5{{x}^{2}}-4{{y}^{2}}=8\] done
clear
View Solution play_arrow
-
question_answer17)
The eccentricity of the hyperbola can never be equal to
A)
\[\sqrt{\frac{9}{5}}\] done
clear
B)
\[2\sqrt{\frac{1}{9}}\] done
clear
C)
\[3\sqrt{\frac{1}{8}}\] done
clear
D)
\[2\] done
clear
View Solution play_arrow
-
question_answer18)
A hyperbola passes through the points (3, 2) and (?17, 12) and has its centre at origin and transverse axis is along x-axis. The length of its transverse axis is
A)
2 done
clear
B)
4 done
clear
C)
6 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer19)
The locus of the point of intersection of the lines \[\sqrt{3}x-y-4\sqrt{3}k=0\] and \[\sqrt{3}kx+ky-4\sqrt{3}=0\] for different value of k is
A)
Circle done
clear
B)
Parabola done
clear
C)
Hyperbola done
clear
D)
Ellipse done
clear
View Solution play_arrow
-
question_answer20)
The difference of the focal distance of any point on the hyperbola \[9{{x}^{2}}-16{{y}^{2}}=144\], is [MP PET 1995; Orissa JEE 2004]
A)
8 done
clear
B)
7 done
clear
C)
6 done
clear
D)
4 done
clear
View Solution play_arrow
-
question_answer21)
The eccentricity of the hyperbola \[4{{x}^{2}}-9{{y}^{2}}=16\], is
A)
\[\frac{8}{3}\] done
clear
B)
\[\frac{5}{4}\] done
clear
C)
\[\frac{\sqrt{13}}{3}\] done
clear
D)
\[\frac{4}{3}\] done
clear
View Solution play_arrow
-
question_answer22)
The eccentricity of the conic \[{{x}^{2}}-4{{y}^{2}}=1\], is [MP PET 1999]
A)
\[\frac{2}{\sqrt{3}}\] done
clear
B)
\[\frac{\sqrt{3}}{2}\] done
clear
C)
\[\frac{2}{\sqrt{5}}\] done
clear
D)
\[\frac{\sqrt{5}}{2}\] done
clear
View Solution play_arrow
-
question_answer23)
The locus of the centre of a circle, which touches externally the given two circles, is [Karnataka CET 1999]
A)
Circle done
clear
B)
Parabola done
clear
C)
Hyperbola done
clear
D)
Ellipse done
clear
View Solution play_arrow
-
question_answer24)
The foci of the hyperbola \[2{{x}^{2}}-3{{y}^{2}}=5\], is [MP PET 2000]
A)
\[\left( \pm \frac{5}{\sqrt{6}},\ 0 \right)\] done
clear
B)
\[\left( \pm \frac{5}{6},\ 0 \right)\] done
clear
C)
\[\left( \pm \frac{\sqrt{5}}{6},\ 0 \right)\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer25)
The latus-rectum of the hyperbola \[16{{x}^{2}}-9{{y}^{2}}=\] \[144\], is [MP PET 2000]
A)
\[\frac{16}{3}\] done
clear
B)
\[\frac{32}{3}\] done
clear
C)
\[\frac{8}{3}\] done
clear
D)
\[\frac{4}{3}\] done
clear
View Solution play_arrow
-
question_answer26)
The foci of the hyperbola \[9{{x}^{2}}-16{{y}^{2}}=144\] are [MP PET 2001]
A)
\[(\pm 4,\ 0)\] done
clear
B)
\[(0,\ \pm 4)\] done
clear
C)
\[(\pm 5,\ 0)\] done
clear
D)
\[(0,\ \pm 5)\] done
clear
View Solution play_arrow
-
question_answer27)
The length of transverse axis of the parabola \[3{{x}^{2}}-4{{y}^{2}}=32\] is [Karnataka CET 2001]
A)
\[\frac{8\sqrt{2}}{\sqrt{3}}\] done
clear
B)
\[\frac{16\sqrt{2}}{\sqrt{3}}\] done
clear
C)
\[\frac{3}{32}\] done
clear
D)
\[\frac{64}{3}\] done
clear
View Solution play_arrow
-
question_answer28)
The directrix of the hyperbola is \[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{4}=1\] [UPSEAT 2003]
A)
\[x=9/\sqrt{13}\] done
clear
B)
\[y=9/\sqrt{13}\] done
clear
C)
\[x=6/\sqrt{13}\] done
clear
D)
\[y=6/\sqrt{13}\] done
clear
View Solution play_arrow
-
question_answer29)
Locus of the point of intersection of straight lines \[\frac{x}{a}-\frac{y}{b}=m\] and \[\frac{x}{a}+\frac{y}{b}=\frac{1}{m}\] is [MP PET 1991, 2003]
A)
An ellipse done
clear
B)
A circle done
clear
C)
A hyperbola done
clear
D)
A parabola done
clear
View Solution play_arrow
-
question_answer30)
The locus of a point which moves such that the difference of its distances from two fixed points is always a constant is [Karnataka CET 2003]
A)
A straight line done
clear
B)
A circle done
clear
C)
An ellipse done
clear
D)
A hyperbola done
clear
View Solution play_arrow
-
question_answer31)
The eccentricity of the hyperbola \[2{{x}^{2}}-{{y}^{2}}=6\] is [MP PET 1992]
A)
\[\sqrt{2}\] done
clear
B)
2 done
clear
C)
3 done
clear
D)
\[\sqrt{3}\] done
clear
View Solution play_arrow
-
question_answer32)
The distance between the foci of a hyperbola is double the distance between its vertices and the length of its conjugate axis is 6. The equation of the hyperbola referred to its axes as axes of co-ordinates is
A)
\[3{{x}^{2}}-{{y}^{2}}=3\] done
clear
B)
\[{{x}^{2}}-3{{y}^{2}}=3\] done
clear
C)
\[3{{x}^{2}}-{{y}^{2}}=9\] done
clear
D)
\[{{x}^{2}}-3{{y}^{2}}=9\] done
clear
View Solution play_arrow
-
question_answer33)
The equation \[13[{{(x-1)}^{2}}+{{(y-2)}^{2}}]=3{{(2x+3y-2)}^{2}}\] represents
A)
Parabola done
clear
B)
Ellipse done
clear
C)
Hyperbola done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer34)
The equation of the hyperbola whose directrix is \[x+2y=1\], focus (2, 1) and eccentricity 2 will be [MP PET 1988, 89]
A)
\[{{x}^{2}}-16xy-11{{y}^{2}}-12x+6y+21=0\] done
clear
B)
\[3{{x}^{2}}+16xy+15{{y}^{2}}-4x-14y-1=0\] done
clear
C)
\[{{x}^{2}}+16xy+11{{y}^{2}}-12x-6y+21=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer35)
The vertices of a hyperbola are at (0, 0) and (10, 0) and one of its foci is at (18, 0). The equation of the hyperbola is
A)
\[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{144}=1\] done
clear
B)
\[\frac{{{(x-5)}^{2}}}{25}-\frac{{{y}^{2}}}{144}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{25}-\frac{{{(y-5)}^{2}}}{144}=1\] done
clear
D)
\[\frac{{{(x-5)}^{2}}}{25}-\frac{{{(y-5)}^{2}}}{144}=1\] done
clear
View Solution play_arrow
-
question_answer36)
The equation \[{{x}^{2}}+4xy+{{y}^{2}}+2x+4y+2=0\] represents
A)
An ellipse done
clear
B)
A pair of straight lines done
clear
C)
A hyperbola done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer37)
The equation of the directrices of the conic \[{{x}^{2}}+2x-{{y}^{2}}+5=0\] are
A)
\[x=\pm 1\] done
clear
B)
\[y=\pm 2\] done
clear
C)
\[y=\pm \sqrt{2}\] done
clear
D)
\[x=\pm \sqrt{3}\] done
clear
View Solution play_arrow
-
question_answer38)
Foci of the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{(y-2)}^{2}}}{9}=1\] are
A)
(5, 2) (?5, 2) done
clear
B)
(5, 2) (5, ?2) done
clear
C)
(5, 2) (?5, ?2) done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer39)
Centre of hyperbola \[9{{x}^{2}}-16{{y}^{2}}+18x+32y-151=0\] is
A)
(1, ?1) done
clear
B)
(?1, 1) done
clear
C)
(?1, ?1) done
clear
D)
(1, 1) done
clear
View Solution play_arrow
-
question_answer40)
The equation of the hyperbola whose foci are (6, 4) and (?4, 4) and eccentricity 2 is given by [MP PET 1993]
A)
\[12{{x}^{2}}-4{{y}^{2}}-24x+32y-127=0\] done
clear
B)
\[12{{x}^{2}}+4{{y}^{2}}+24x-32y-127=0\] done
clear
C)
\[12{{x}^{2}}-4{{y}^{2}}-24x-32y+127=0\] done
clear
D)
\[12{{x}^{2}}-4{{y}^{2}}+24x+32y+127=0\] done
clear
View Solution play_arrow
-
question_answer41)
The auxiliary equation of circle of hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], is
A)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}={{b}^{2}}\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] done
clear
View Solution play_arrow
-
question_answer42)
The equation \[{{x}^{2}}-16xy-11{{y}^{2}}-12x+6y+21=0\] represents
A)
Parabola done
clear
B)
Ellipse done
clear
C)
Hyperbola done
clear
D)
Two straight lines done
clear
View Solution play_arrow
-
question_answer43)
The latus rectum of the hyperbola \[9{{x}^{2}}-16{{y}^{2}}-18x-32y-151=0\] is [MP PET 1996]
A)
\[\frac{9}{4}\] done
clear
B)
9 done
clear
C)
\[\frac{3}{2}\] done
clear
D)
\[\frac{9}{2}\] done
clear
View Solution play_arrow
-
question_answer44)
The equation of the hyperbola whose directrix is \[2x+y=1\], focus (1, 1) and eccentricity \[=\sqrt{3}\], is
A)
\[7{{x}^{2}}+12xy-2{{y}^{2}}-2x+4y-7=0\] done
clear
B)
\[11{{x}^{2}}+12xy+2{{y}^{2}}-10x-4y+1=0\] done
clear
C)
\[11{{x}^{2}}+12xy+2{{y}^{2}}-14x-14y+1=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer45)
\[{{x}^{2}}-4{{y}^{2}}-2x+16y-40=0\] represents [DCE 1999]
A)
A pair of straight lines done
clear
B)
An ellipse done
clear
C)
A hyperbola done
clear
D)
A parabola done
clear
View Solution play_arrow
-
question_answer46)
The distance between the directrices of the hyperbola \[x=8\sec \theta ,\ \ y=8\tan \theta \] is [Karnataka CET 2003]
A)
\[16\sqrt{2}\] done
clear
B)
\[\sqrt{2}\] done
clear
C)
\[8\sqrt{2}\] done
clear
D)
\[4\sqrt{2}\] done
clear
View Solution play_arrow
-
question_answer47)
The eccentricity of the hyperbola \[5{{x}^{2}}-4{{y}^{2}}+20x+8y=4\] is [UPSEAT 2004]
A)
\[\sqrt{2}\] done
clear
B)
\[\frac{3}{2}\] done
clear
C)
2 done
clear
D)
3 done
clear
View Solution play_arrow
-
question_answer48)
The latus rectum of the hyperbola \[9{{x}^{2}}-16{{y}^{2}}+72x-32y-16=0\] is [Pb. CET 2004]
A)
\[\frac{9}{2}\] done
clear
B)
\[-\frac{9}{2}\] done
clear
C)
\[\frac{32}{3}\] done
clear
D)
\[-\frac{32}{3}\] done
clear
View Solution play_arrow
-
question_answer49)
The point of contact of the tangent \[y=x+2\] to the hyperbola \[5{{x}^{2}}-9{{y}^{2}}=45\] is
A)
(9/2, 5/2) done
clear
B)
(5/2, 9/2) done
clear
C)
(?9/2, ?5/2) done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer50)
The line \[lx+my+n=0\] will be a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], if [MP PET 2001]
A)
\[{{a}^{2}}{{l}^{2}}+{{b}^{2}}{{m}^{2}}={{n}^{2}}\] done
clear
B)
\[{{a}^{2}}{{l}^{2}}-{{b}^{2}}{{m}^{2}}={{n}^{2}}\] done
clear
C)
\[a{{m}^{2}}-{{b}^{2}}{{n}^{2}}={{a}^{2}}{{l}^{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer51)
If the line \[y=2x+\lambda \] be a tangent to the hyperbola \[36{{x}^{2}}-25{{y}^{2}}=3600\], then \[\lambda =\]
A)
16 done
clear
B)
?16 done
clear
C)
\[\pm 16\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer52)
The line \[3x-4y=5\]is a tangent to the hyperbola\[{{x}^{2}}-4{{y}^{2}}=5\]. The point of contact is
A)
(3, 1) done
clear
B)
(2, 1/4) done
clear
C)
(1, 3) done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer53)
The equation of the tangent at the point \[(a\sec \theta ,\ b\tan \theta )\] of the conic \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], is
A)
\[x{{\sec }^{2}}\theta -y{{\tan }^{2}}\theta =1\] done
clear
B)
\[\frac{x}{a}\sec \theta -\frac{y}{b}\tan \theta =1\] done
clear
C)
\[\frac{x+a\sec \theta }{{{a}^{2}}}-\frac{y+b\tan \theta }{{{b}^{2}}}=1\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer54)
The equation of the tangents to the conic \[3{{x}^{2}}-{{y}^{2}}=3\] perpendicular to the line \[x+3y=2\] is
A)
\[y=3x\pm \sqrt{6}\] done
clear
B)
\[y=6x\pm \sqrt{3}\] done
clear
C)
\[y=x\pm \sqrt{6}\] done
clear
D)
\[y=3x\pm 6\] done
clear
View Solution play_arrow
-
question_answer55)
The equation of the tangent to the hyperbola \[2{{x}^{2}}-3{{y}^{2}}=6\]which is parallel to the line \[y=3x+4\], is [MNR 1993]
A)
\[y=3x+5\] done
clear
B)
\[y=3x-5\] done
clear
C)
\[y=3x+5\]and\[y=3x-5\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer56)
The locus of the point of intersection of any two perpendicular tangents to the hyperbola is a circle which is called the director circle of the hyperbola, then the eqn of this circle is
A)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}=2ab\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer57)
The equation of the tangents to the hyperbola \[3{{x}^{2}}-4{{y}^{2}}=12\] which cuts equal intercepts from the axes, are
A)
\[y+x=\pm 1\] done
clear
B)
\[y-x=\pm 1\] done
clear
C)
\[3x+4y=\pm 1\] done
clear
D)
\[3x-4y=\pm 1\] done
clear
View Solution play_arrow
-
question_answer58)
If \[{{m}_{1}}\] and \[{{m}_{2}}\]are the slopes of the tangents to the hyperbola \[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{16}=1\] which pass through the point (6, 2), then
A)
\[{{m}_{1}}+{{m}_{2}}=\frac{24}{11}\] done
clear
B)
\[{{m}_{1}}{{m}_{2}}=\frac{20}{11}\] done
clear
C)
\[{{m}_{1}}+{{m}_{2}}=\frac{48}{11}\] done
clear
D)
\[{{m}_{1}}{{m}_{2}}=\frac{11}{20}\] done
clear
View Solution play_arrow
-
question_answer59)
The equation of the tangent to the hyperbola \[4{{y}^{2}}={{x}^{2}}-1\] at the point (1, 0) is [Karnataka CET 1994]
A)
\[x=1\] done
clear
B)
\[y=1\] done
clear
C)
\[y=4\] done
clear
D)
\[x=4\] done
clear
View Solution play_arrow
-
question_answer60)
The value of m for which \[y=mx+6\] is a tangent to the hyperbola \[\frac{{{x}^{2}}}{100}-\frac{{{y}^{2}}}{49}=1\], is [Karnataka CET 1993]
A)
\[\sqrt{\frac{17}{20}}\] done
clear
B)
\[\sqrt{\frac{20}{17}}\] done
clear
C)
\[\sqrt{\frac{3}{20}}\] done
clear
D)
\[\sqrt{\frac{20}{3}}\] done
clear
View Solution play_arrow
-
question_answer61)
The equation of the tangent to the conic \[{{x}^{2}}-{{y}^{2}}-8x+2y+11=0\] at (2, 1) is [Karnataka CET 1993]
A)
\[x+2=0\] done
clear
B)
\[2x+1=0\] done
clear
C)
\[x-2=0\] done
clear
D)
\[x+y+1=0\] done
clear
View Solution play_arrow
-
question_answer62)
The point of contact of the line \[y=x-1\] with \[3{{x}^{2}}-4{{y}^{2}}=12\] is [BIT Mesra 1996]
A)
(4, 3) done
clear
B)
(3, 4) done
clear
C)
(4, ?3) done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer63)
If the straight line \[x\cos \alpha +y\sin \alpha =p\] be a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then [Karnataka CET 1999]
A)
\[{{a}^{2}}{{\cos }^{2}}\alpha +{{b}^{2}}{{\sin }^{2}}\alpha ={{p}^{2}}\] done
clear
B)
\[{{a}^{2}}{{\cos }^{2}}\alpha -{{b}^{2}}{{\sin }^{2}}\alpha ={{p}^{2}}\] done
clear
C)
\[{{a}^{2}}{{\sin }^{2}}\alpha +{{b}^{2}}{{\cos }^{2}}\alpha ={{p}^{2}}\] done
clear
D)
\[{{a}^{2}}{{\sin }^{2}}\alpha -{{b}^{2}}{{\cos }^{2}}\alpha ={{p}^{2}}\] done
clear
View Solution play_arrow
-
question_answer64)
If the tangent on the point \[(2\sec \varphi ,\ 3\tan \varphi )\] of the hyperbola \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{9}=1\] is parallel to \[3x-y+4=0\], then the value of f is [MP PET 1998]
A)
\[{{45}^{o}}\] done
clear
B)
\[{{60}^{o}}\] done
clear
C)
\[{{30}^{o}}\] done
clear
D)
\[{{75}^{o}}\] done
clear
View Solution play_arrow
-
question_answer65)
The radius of the director circle of the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], is [MP PET 1999]
A)
\[a-b\] done
clear
B)
\[\sqrt{a-b}\] done
clear
C)
\[\sqrt{{{a}^{2}}-{{b}^{2}}}\] done
clear
D)
\[\sqrt{{{a}^{2}}+{{b}^{2}}}\] done
clear
View Solution play_arrow
-
question_answer66)
What is the slope of the tangent line drawn to the hyperbola \[xy=a\,(a\ne 0)\] at the point (a, 1) [AMU 2000]
A)
1/a done
clear
B)
?1/a done
clear
C)
a done
clear
D)
? a done
clear
View Solution play_arrow
-
question_answer67)
The line \[y=mx+c\] touches the curve \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], if [Kerala (Engg.) 2002]
A)
\[{{c}^{2}}={{a}^{2}}{{m}^{2}}+{{b}^{2}}\] done
clear
B)
\[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}\] done
clear
C)
\[{{c}^{2}}={{b}^{2}}{{m}^{2}}-{{a}^{2}}\] done
clear
D)
\[{{a}^{2}}={{b}^{2}}{{m}^{2}}+{{c}^{2}}\] done
clear
View Solution play_arrow
-
question_answer68)
The straight line \[x+y=\sqrt{2}p\]will touch the hyperbola \[4{{x}^{2}}-9{{y}^{2}}=36\], if [Orissa JEE 2003]
A)
\[{{p}^{2}}=2\] done
clear
B)
\[{{p}^{2}}=5\] done
clear
C)
\[5{{p}^{2}}=2\] done
clear
D)
\[2{{p}^{2}}=5\] done
clear
View Solution play_arrow
-
question_answer69)
The equation of the director circle of the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{4}=1\] is given by [Karnataka CET 2004]
A)
\[{{x}^{2}}+{{y}^{2}}=16\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}=4\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}=20\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}=12\] done
clear
View Solution play_arrow
-
question_answer70)
The equation of the tangent parallel to \[y-x+5=0\] drawn to \[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\] is [UPSEAT 2004]
A)
\[x-y-1=0\] done
clear
B)
\[x-y+2=0\] done
clear
C)
\[x+y-1=0\] done
clear
D)
\[x+y+2=0\] done
clear
View Solution play_arrow
-
question_answer71)
Let E be the ellipse \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\] and C be the circle\[{{x}^{2}}+{{y}^{2}}=9\]. Let P and Q be the points (1, 2) and (2, 1) respectively. Then [IIT 1994]
A)
Q lies inside C but outside E done
clear
B)
Q lies outside both C and E done
clear
C)
P lies inside both C and E done
clear
D)
P lies inside C but outside E done
clear
View Solution play_arrow
-
question_answer72)
The length of the chord of the parabola \[{{y}^{2}}=4ax\] which passes through the vertex and makes an angle \[\theta \] with the axis of the parabola, is
A)
\[4a\cos \theta \,\text{cose}{{\text{c}}^{2}}\,\theta \] done
clear
B)
\[4a{{\cos }^{2}}\theta \,\text{cosec}\,\theta \] done
clear
C)
\[a\cos \theta \,\text{cose}{{\text{c}}^{2}}\,\theta \] done
clear
D)
\[a{{\cos }^{2}}\theta \,\text{cosec}\,\theta \] done
clear
View Solution play_arrow
-
question_answer73)
The equation of the normal at the point \[(a\sec \theta ,\ b\tan \theta )\] of the curve \[{{b}^{2}}{{x}^{2}}-{{a}^{2}}{{y}^{2}}={{a}^{2}}{{b}^{2}}\] is [Karnataka CET 1999]
A)
\[\frac{ax}{\cos \theta }+\frac{by}{\sin \theta }={{a}^{2}}+{{b}^{2}}\] done
clear
B)
\[\frac{ax}{\tan \theta }+\frac{by}{\sec \theta }={{a}^{2}}+{{b}^{2}}\] done
clear
C)
\[\frac{ax}{\sec \theta }+\frac{by}{\tan \theta }={{a}^{2}}+{{b}^{2}}\] done
clear
D)
\[\frac{ax}{\sec \theta }+\frac{by}{\tan \theta }={{a}^{2}}-{{b}^{2}}\] done
clear
View Solution play_arrow
-
question_answer74)
The condition that the straight line \[lx+my=n\] may be a normal to the hyperbola \[{{b}^{2}}{{x}^{2}}-{{a}^{2}}{{y}^{2}}={{a}^{2}}{{b}^{2}}\] is given by [MP PET 1993, 94]
A)
\[\frac{{{a}^{2}}}{{{l}^{2}}}-\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{({{a}^{2}}+{{b}^{2}})}^{2}}}{{{n}^{2}}}\] done
clear
B)
\[\frac{{{l}^{2}}}{{{a}^{2}}}-\frac{{{m}^{2}}}{{{b}^{2}}}=\frac{{{({{a}^{2}}+{{b}^{2}})}^{2}}}{{{n}^{2}}}\] done
clear
C)
\[\frac{{{a}^{2}}}{{{l}^{2}}}+\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{({{a}^{2}}-{{b}^{2}})}^{2}}}{{{n}^{2}}}\] done
clear
D)
\[\frac{{{l}^{2}}}{{{a}^{2}}}+\frac{{{m}^{2}}}{{{b}^{2}}}=\frac{{{({{a}^{2}}-{{b}^{2}})}^{2}}}{{{n}^{2}}}\] done
clear
View Solution play_arrow
-
question_answer75)
The equation of the normal to the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\] at the point \[(8,\ 3\sqrt{3})\] is [MP PET 1996]
A)
\[\sqrt{3}x+2y=25\] done
clear
B)
\[x+y=25\] done
clear
C)
\[y+2x=25\] done
clear
D)
\[2x+\sqrt{3}y=25\] done
clear
View Solution play_arrow
-
question_answer76)
The equation of the normal at the point (6, 4) on the hyperbola \[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{16}=3\], is
A)
\[3x+8y=50\] done
clear
B)
\[3x-8y=50\] done
clear
C)
\[8x+3y=50\] done
clear
D)
\[8x-3y=50\] done
clear
View Solution play_arrow
-
question_answer77)
What will be equation of that chord of hyperbola \[25{{x}^{2}}-16{{y}^{2}}=400\], whose mid point is (5, 3) [UPSEAT 1999]
A)
\[115x-117y=17\] done
clear
B)
\[125x-48y=481\] done
clear
C)
\[127x+33y=341\] done
clear
D)
\[15x+121y=105\] done
clear
View Solution play_arrow
-
question_answer78)
The value of m, for which the line \[y=mx+\frac{25\sqrt{3}}{3}\], is a normal to the conic \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\], is [MP PET 2004]
A)
\[\sqrt{3}\] done
clear
B)
\[-\frac{2}{\sqrt{3}}\] done
clear
C)
\[-\frac{\sqrt{3}}{2}\] done
clear
D)
1 done
clear
View Solution play_arrow
-
question_answer79)
The equation of the normal to the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\] at \[(-4,\ 0)\] is [UPSEAT 2002]
A)
\[y=0\] done
clear
B)
\[y=x\] done
clear
C)
\[x=0\] done
clear
D)
\[x=-y\] done
clear
View Solution play_arrow
-
question_answer80)
The eccentricity of the conjugate hyperbola of the hyperbola \[{{x}^{2}}-3{{y}^{2}}=1\], is [MP PET 1999]
A)
2 done
clear
B)
\[\frac{2}{\sqrt{3}}\] done
clear
C)
4 done
clear
D)
\[\frac{4}{3}\] done
clear
View Solution play_arrow
-
question_answer81)
If e and e? are eccentricities of hyperbola and its conjugate respectively, then [UPSEAT 1999]
A)
\[{{\left( \frac{1}{e} \right)}^{2}}+{{\left( \frac{1}{e'} \right)}^{2}}=1\] done
clear
B)
\[\frac{1}{e}+\frac{1}{e'}=1\] done
clear
C)
\[{{\left( \frac{1}{e} \right)}^{2}}+{{\left( \frac{1}{e'} \right)}^{2}}=0\] done
clear
D)
\[\frac{1}{e}+\frac{1}{e'}=2\] done
clear
View Solution play_arrow
-
question_answer82)
The product of the lengths of perpendiculars drawn from any point on the hyperbola \[{{x}^{2}}-2{{y}^{2}}-2=0\] to its asymptotes is [EAMCET 2003]
A)
1/2 done
clear
B)
2/3 done
clear
C)
3/2 done
clear
D)
2 done
clear
View Solution play_arrow
-
question_answer83)
The equation of a hyperbola, whose foci are (5, 0) and (?5, 0) and the length of whose conjugate axis is 8, is
A)
\[9{{x}^{2}}-16{{y}^{2}}=144\] done
clear
B)
\[16{{x}^{2}}-9{{y}^{2}}=144\] done
clear
C)
\[9{{x}^{2}}+16{{y}^{2}}=144\] done
clear
D)
\[16{{x}^{2}}-9{{y}^{2}}=12\] done
clear
View Solution play_arrow
-
question_answer84)
The equation of the hyperbola whose foci are the foci of the ellipse \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{9}=1\] and the eccentricity is 2, is
A)
\[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{12}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{12}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{12}+\frac{{{y}^{2}}}{4}=1\] done
clear
D)
\[\frac{{{x}^{2}}}{12}-\frac{{{y}^{2}}}{4}=1\] done
clear
View Solution play_arrow
-
question_answer85)
The coordinates of the foci of the rectangular hyperbola \[xy={{c}^{2}}\] are
A)
\[(\pm c,\ \pm c)\] done
clear
B)
\[(\pm c\sqrt{2},\ \pm c\sqrt{2})\] done
clear
C)
\[\left( \pm \frac{c}{\sqrt{2}},\ \pm \frac{c}{\sqrt{2}} \right)\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer86)
The eccentricity of curve \[{{x}^{2}}-{{y}^{2}}=1\] is [MP PET 1995]
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{1}{\sqrt{2}}\] done
clear
C)
2 done
clear
D)
\[\sqrt{2}\] done
clear
View Solution play_arrow
-
question_answer87)
The locus of the point of intersection of lines \[(x+y)t=a\] and \[x-y=at\], where t is the parameter, is
A)
A circle done
clear
B)
An ellipse done
clear
C)
A rectangular hyperbola done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer88)
The equation of the hyperbola referred to its axes as axes of coordinate and whose distance between the foci is 16 and eccentricity is \[\sqrt{2}\], is [MNR 1984]
A)
\[{{x}^{2}}-{{y}^{2}}=16\] done
clear
B)
\[{{x}^{2}}-{{y}^{2}}=32\] done
clear
C)
\[{{x}^{2}}-2{{y}^{2}}=16\] done
clear
D)
\[{{y}^{2}}-{{x}^{2}}=16\] done
clear
View Solution play_arrow
-
question_answer89)
If the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and the hyperbola \[\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25}\] coincide, then the value of \[{{b}^{2}}\] is [MNR 1992; UPSEAT 2001; AIEEE 2003; Karnataka CET 2004; Kerala (Engg.) 2005]
A)
1 done
clear
B)
5 done
clear
C)
7 done
clear
D)
9 done
clear
View Solution play_arrow
-
question_answer90)
A tangent to a hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] intercepts a length of unity from each of the co-ordinate axes, then the point (a, b) lies on the rectangular hyperbola
A)
\[{{x}^{2}}-{{y}^{2}}=2\] done
clear
B)
\[{{x}^{2}}-{{y}^{2}}=1\] done
clear
C)
\[{{x}^{2}}-{{y}^{2}}=-1\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer91)
Curve \[xy={{c}^{2}}\] is said to be
A)
Parabola done
clear
B)
Rectangular hyperbola done
clear
C)
Hyperbola done
clear
D)
Ellipse done
clear
View Solution play_arrow
-
question_answer92)
The reciprocal of the eccentricity of rectangular hyperbola, is [MP PET 1994]
A)
2 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\sqrt{2}\] done
clear
D)
\[\frac{1}{\sqrt{2}}\] done
clear
View Solution play_arrow
-
question_answer93)
The eccentricity of the hyperbola \[\frac{\sqrt{1999}}{3}({{x}^{2}}-{{y}^{2}})=1\] is [Karnataka CET 1999]
A)
\[\sqrt{3}\] done
clear
B)
\[\sqrt{2}\] done
clear
C)
2 done
clear
D)
\[2\sqrt{2}\] done
clear
View Solution play_arrow
-
question_answer94)
If transverse and conjugate axes of a hyperbola are equal, then its eccentricity is [MP PET 2003]
A)
\[\sqrt{3}\] done
clear
B)
\[\sqrt{2}\] done
clear
C)
\[1/\sqrt{2}\] done
clear
D)
2 done
clear
View Solution play_arrow
-
question_answer95)
If \[5{{x}^{2}}+\lambda {{y}^{2}}=20\] represents a rectangular hyperbola, then \[\lambda \] equals
A)
5 done
clear
B)
4 done
clear
C)
?5 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer96)
The equation of the hyperbola referred to the axis as axes of co-ordinate and whose distance between the foci is 16 and eccentricity is \[\sqrt{2}\], is [UPSEAT 2000]
A)
\[{{x}^{2}}-{{y}^{2}}=16\] done
clear
B)
\[{{x}^{2}}-{{y}^{2}}=32\] done
clear
C)
\[{{x}^{2}}-2{{y}^{2}}=16\] done
clear
D)
\[{{y}^{2}}-{{x}^{2}}=16\] done
clear
View Solution play_arrow
-
question_answer97)
If e and e? are the eccentricities of the ellipse \[5{{x}^{2}}+9{{y}^{2}}=45\] and the hyperbola \[5{{x}^{2}}-4{{y}^{2}}=45\] respectively, then \[ee'=\] [EAMCET 2002]
A)
9 done
clear
B)
4 done
clear
C)
5 done
clear
D)
1 done
clear
View Solution play_arrow
-
question_answer98)
The distance between the directrices of a rectangular hyperbola is 10 units, then distance between its foci is [MP PET 2002]
A)
\[10\sqrt{2}\] done
clear
B)
5 done
clear
C)
\[5\sqrt{2}\] done
clear
D)
20 done
clear
View Solution play_arrow
-
question_answer99)
Eccentricity of the curve \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\] is [UPSEAT 2002]
A)
2 done
clear
B)
\[\sqrt{2}\] done
clear
C)
4 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer100)
Eccentricity of rectangular hyperbola is [UPSEAT 2002]
A)
\[\frac{1}{\sqrt{2}}\] done
clear
B)
\[\frac{-1}{\sqrt{2}}\] done
clear
C)
\[\sqrt{2}\] done
clear
D)
> 2 done
clear
View Solution play_arrow
-
question_answer101)
The eccentricity of the hyperbola conjugate to \[{{x}^{2}}-3{{y}^{2}}=2x+8\] is [UPSEAT 2004]
A)
\[\frac{2}{\sqrt{3}}\] done
clear
B)
\[\sqrt{3}\] done
clear
C)
2 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer102)
The locus of a point \[P(\alpha ,\,\beta )\] moving under the condition that the line \[y=\alpha x+\beta \] is a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is [AIEEE 2005]
A)
A parabola done
clear
B)
A hyperbola done
clear
C)
An ellipse done
clear
D)
A circle done
clear
View Solution play_arrow
-
question_answer103)
The eccentricity of the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{25}=1\] is [Karnataka CET 2005]
A)
3/4 done
clear
B)
3/5 done
clear
C)
\[\sqrt{41}/4\] done
clear
D)
\[\sqrt{41/5}\] done
clear
View Solution play_arrow
-
question_answer104)
The equation to the hyperbola having its eccentricity 2 and the distance between its foci is 8 [Karnataka CET 2005]
A)
\[\frac{{{x}^{2}}}{12}-\frac{{{y}^{2}}}{4}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{12}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{8}-\frac{{{y}^{2}}}{2}=1\] done
clear
D)
\[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\] done
clear
View Solution play_arrow
-
question_answer105)
If q is the acute angle of intersection at a real point of intersection of the circle \[{{x}^{2}}+{{y}^{2}}=5\] and the parabola \[{{y}^{2}}=4x\] then tanq is equal to [Karnataka CET 2005]
A)
1 done
clear
B)
\[\sqrt{3}\] done
clear
C)
3 done
clear
D)
\[\frac{1}{\sqrt{3}}\] done
clear
View Solution play_arrow
-
question_answer106)
The equation of the hyperbola in the standard form (with transverse axis along the x-axis) having the length of the latus rectum = 9 units and eccentricity = 5/4 is [Kerala (Engg.) 2005]
A)
\[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{18}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{36}-\frac{{{y}^{2}}}{27}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{64}-\frac{{{y}^{2}}}{36}=1\] done
clear
D)
\[\frac{{{x}^{2}}}{36}-\frac{{{y}^{2}}}{64}=1\] done
clear
E)
\[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\] done
clear
View Solution play_arrow
-
question_answer107)
If \[4{{x}^{2}}+p{{y}^{2}}=45\] and \[{{x}^{2}}-4{{y}^{2}}=5\] cut orthogonally, then the value of p is [Kerala (Engg.) 2005]
A)
1/9 done
clear
B)
1/3 done
clear
C)
3 done
clear
D)
18 done
clear
E)
9 done
clear
View Solution play_arrow
-
question_answer108)
Find the equation of axis of the given hyperbola \[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\] which is equally inclined to the axes [DCE 2005]
A)
\[y=x+1\] done
clear
B)
\[y=x-1\] done
clear
C)
\[y=x+2\] done
clear
D)
\[y=x-2\] done
clear
View Solution play_arrow