MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 4301. |
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. | \[{{x}^{2}}-{{y}^{2}}=16\] |
| B. | \[{{x}^{2}}-{{y}^{2}}=32\] |
| C. | \[{{x}^{2}}-2{{y}^{2}}=16\] |
| D. | \[{{y}^{2}}-{{x}^{2}}=16\] |
| Answer» C. \[{{x}^{2}}-2{{y}^{2}}=16\] | |
| 4302. |
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 |
| B. | 4 |
| C. | 5 |
| D. | 1 |
| Answer» E. | |
| 4303. |
If \[5{{x}^{2}}+\lambda {{y}^{2}}=20\] represents a rectangular hyperbola, then \[\lambda \] equals |
| A. | 5 |
| B. | 4 |
| C. | ?5 |
| D. | None of these |
| Answer» D. None of these | |
| 4304. |
If transverse and conjugate axes of a hyperbola are equal, then its eccentricity is [MP PET 2003] |
| A. | \[\sqrt{3}\] |
| B. | \[\sqrt{2}\] |
| C. | \[1/\sqrt{2}\] |
| D. | 2 |
| Answer» C. \[1/\sqrt{2}\] | |
| 4305. |
The eccentricity of the hyperbola \[\frac{\sqrt{1999}}{3}({{x}^{2}}-{{y}^{2}})=1\] is [Karnataka CET 1999] |
| A. | \[\sqrt{3}\] |
| B. | \[\sqrt{2}\] |
| C. | 2 |
| D. | \[2\sqrt{2}\] |
| Answer» C. 2 | |
| 4306. |
Curve \[xy={{c}^{2}}\] is said to be |
| A. | Parabola |
| B. | Rectangular hyperbola |
| C. | Hyperbola |
| D. | Ellipse |
| Answer» C. Hyperbola | |
| 4307. |
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. | \[{{x}^{2}}-{{y}^{2}}=2\] |
| B. | \[{{x}^{2}}-{{y}^{2}}=1\] |
| C. | \[{{x}^{2}}-{{y}^{2}}=-1\] |
| D. | None of these |
| Answer» C. \[{{x}^{2}}-{{y}^{2}}=-1\] | |
| 4308. |
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 |
| B. | 5 |
| C. | 7 |
| D. | 9 |
| Answer» D. 9 | |
| 4309. |
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. | \[{{x}^{2}}-{{y}^{2}}=16\] |
| B. | \[{{x}^{2}}-{{y}^{2}}=32\] |
| C. | \[{{x}^{2}}-2{{y}^{2}}=16\] |
| D. | \[{{y}^{2}}-{{x}^{2}}=16\] |
| Answer» C. \[{{x}^{2}}-2{{y}^{2}}=16\] | |
| 4310. |
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 |
| B. | An ellipse |
| C. | A rectangular hyperbola |
| D. | None of these |
| Answer» D. None of these | |
| 4311. |
The coordinates of the foci of the rectangular hyperbola \[xy={{c}^{2}}\] are |
| A. | \[(\pm c,\ \pm c)\] |
| B. | \[(\pm c\sqrt{2},\ \pm c\sqrt{2})\] |
| C. | \[\left( \pm \frac{c}{\sqrt{2}},\ \pm \frac{c}{\sqrt{2}} \right)\] |
| D. | None of these |
| Answer» C. \[\left( \pm \frac{c}{\sqrt{2}},\ \pm \frac{c}{\sqrt{2}} \right)\] | |
| 4312. |
The eccentricity of curve \[{{x}^{2}}-{{y}^{2}}=1\] is [MP PET 1995] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{\sqrt{2}}\] |
| C. | 2 |
| D. | \[\sqrt{2}\] |
| Answer» E. | |
| 4313. |
The equation of a hyperbola, whose foci are (5, 0) and (?5, 0) and the length of whose conjugate axis is 8, is |
| A. | \[9{{x}^{2}}-16{{y}^{2}}=144\] |
| B. | \[16{{x}^{2}}-9{{y}^{2}}=144\] |
| C. | \[9{{x}^{2}}+16{{y}^{2}}=144\] |
| D. | \[16{{x}^{2}}-9{{y}^{2}}=12\] |
| Answer» C. \[9{{x}^{2}}+16{{y}^{2}}=144\] | |
| 4314. |
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 |
| B. | 2/3 |
| C. | 3/2 |
| D. | 2 |
| Answer» C. 3/2 | |
| 4315. |
If e and e? are eccentricities of hyperbola and its conjugate respectively, then [UPSEAT 1999] |
| A. | \[{{\left( \frac{1}{e} \right)}^{2}}+{{\left( \frac{1}{e'} \right)}^{2}}=1\] |
| B. | \[\frac{1}{e}+\frac{1}{e'}=1\] |
| C. | \[{{\left( \frac{1}{e} \right)}^{2}}+{{\left( \frac{1}{e'} \right)}^{2}}=0\] |
| D. | \[\frac{1}{e}+\frac{1}{e'}=2\] |
| Answer» B. \[\frac{1}{e}+\frac{1}{e'}=1\] | |
| 4316. |
The eccentricity of the conjugate hyperbola of the hyperbola \[{{x}^{2}}-3{{y}^{2}}=1\], is [MP PET 1999] |
| A. | 2 |
| B. | \[\frac{2}{\sqrt{3}}\] |
| C. | 4 |
| D. | \[\frac{4}{3}\] |
| Answer» B. \[\frac{2}{\sqrt{3}}\] | |
| 4317. |
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. | \[\frac{4}{49}{{x}^{2}}-\frac{196}{51}{{y}^{2}}=1\] |
| B. | \[\frac{49}{4}{{x}^{2}}-\frac{51}{196}{{y}^{2}}=1\] |
| C. | \[\frac{4}{49}{{x}^{2}}-\frac{51}{196}{{y}^{2}}=1\] |
| D. | None of these |
| Answer» D. None of these | |
| 4318. |
The equation of the normal to the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\] at \[(-4,\ 0)\] is [UPSEAT 2002] |
| A. | \[y=0\] |
| B. | \[y=x\] |
| C. | \[x=0\] |
| D. | \[x=-y\] |
| Answer» B. \[y=x\] | |
| 4319. |
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. | \[\sqrt{3}\] |
| B. | \[-\frac{2}{\sqrt{3}}\] |
| C. | \[-\frac{\sqrt{3}}{2}\] |
| D. | 1 |
| Answer» C. \[-\frac{\sqrt{3}}{2}\] | |
| 4320. |
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. | \[115x-117y=17\] |
| B. | \[125x-48y=481\] |
| C. | \[127x+33y=341\] |
| D. | \[15x+121y=105\] |
| Answer» C. \[127x+33y=341\] | |
| 4321. |
The equation of the normal at the point (6, 4) on the hyperbola \[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{16}=3\], is |
| A. | \[3x+8y=50\] |
| B. | \[3x-8y=50\] |
| C. | \[8x+3y=50\] |
| D. | \[8x-3y=50\] |
| Answer» B. \[3x-8y=50\] | |
| 4322. |
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. | \[\sqrt{3}x+2y=25\] |
| B. | \[x+y=25\] |
| C. | \[y+2x=25\] |
| D. | \[2x+\sqrt{3}y=25\] |
| Answer» E. | |
| 4323. |
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. | \[\frac{{{a}^{2}}}{{{l}^{2}}}-\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{({{a}^{2}}+{{b}^{2}})}^{2}}}{{{n}^{2}}}\] |
| B. | \[\frac{{{l}^{2}}}{{{a}^{2}}}-\frac{{{m}^{2}}}{{{b}^{2}}}=\frac{{{({{a}^{2}}+{{b}^{2}})}^{2}}}{{{n}^{2}}}\] |
| C. | \[\frac{{{a}^{2}}}{{{l}^{2}}}+\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{({{a}^{2}}-{{b}^{2}})}^{2}}}{{{n}^{2}}}\] |
| D. | \[\frac{{{l}^{2}}}{{{a}^{2}}}+\frac{{{m}^{2}}}{{{b}^{2}}}=\frac{{{({{a}^{2}}-{{b}^{2}})}^{2}}}{{{n}^{2}}}\] |
| Answer» B. \[\frac{{{l}^{2}}}{{{a}^{2}}}-\frac{{{m}^{2}}}{{{b}^{2}}}=\frac{{{({{a}^{2}}+{{b}^{2}})}^{2}}}{{{n}^{2}}}\] | |
| 4324. |
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. | \[\frac{ax}{\cos \theta }+\frac{by}{\sin \theta }={{a}^{2}}+{{b}^{2}}\] |
| B. | \[\frac{ax}{\tan \theta }+\frac{by}{\sec \theta }={{a}^{2}}+{{b}^{2}}\] |
| C. | \[\frac{ax}{\sec \theta }+\frac{by}{\tan \theta }={{a}^{2}}+{{b}^{2}}\] |
| D. | \[\frac{ax}{\sec \theta }+\frac{by}{\tan \theta }={{a}^{2}}-{{b}^{2}}\] |
| Answer» D. \[\frac{ax}{\sec \theta }+\frac{by}{\tan \theta }={{a}^{2}}-{{b}^{2}}\] | |
| 4325. |
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. | \[4a\cos \theta \,\text{cose}{{\text{c}}^{2}}\,\theta \] |
| B. | \[4a{{\cos }^{2}}\theta \,\text{cosec}\,\theta \] |
| C. | \[a\cos \theta \,\text{cose}{{\text{c}}^{2}}\,\theta \] |
| D. | \[a{{\cos }^{2}}\theta \,\text{cosec}\,\theta \] |
| Answer» B. \[4a{{\cos }^{2}}\theta \,\text{cosec}\,\theta \] | |
| 4326. |
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. | \[x-y-1=0\] |
| B. | \[x-y+2=0\] |
| C. | \[x+y-1=0\] |
| D. | \[x+y+2=0\] |
| Answer» B. \[x-y+2=0\] | |
| 4327. |
The equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13, is |
| A. | \[25{{x}^{2}}-144{{y}^{2}}=900\] |
| B. | \[144{{x}^{2}}-25{{y}^{2}}=900\] |
| C. | \[144{{x}^{2}}+25{{y}^{2}}=900\] |
| D. | \[25{{x}^{2}}+144{{y}^{2}}=900\] |
| Answer» B. \[144{{x}^{2}}-25{{y}^{2}}=900\] | |
| 4328. |
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. | \[{{x}^{2}}+{{y}^{2}}=16\] |
| B. | \[{{x}^{2}}+{{y}^{2}}=4\] |
| C. | \[{{x}^{2}}+{{y}^{2}}=20\] |
| D. | \[{{x}^{2}}+{{y}^{2}}=12\] |
| Answer» E. | |
| 4329. |
The straight line \[x+y=\sqrt{2}p\]will touch the hyperbola \[4{{x}^{2}}-9{{y}^{2}}=36\], if [Orissa JEE 2003] |
| A. | \[{{p}^{2}}=2\] |
| B. | \[{{p}^{2}}=5\] |
| C. | \[5{{p}^{2}}=2\] |
| D. | \[2{{p}^{2}}=5\] |
| Answer» E. | |
| 4330. |
The line \[y=mx+c\] touches the curve \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], if [Kerala (Engg.) 2002] |
| A. | \[{{c}^{2}}={{a}^{2}}{{m}^{2}}+{{b}^{2}}\] |
| B. | \[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}\] |
| C. | \[{{c}^{2}}={{b}^{2}}{{m}^{2}}-{{a}^{2}}\] |
| D. | \[{{a}^{2}}={{b}^{2}}{{m}^{2}}+{{c}^{2}}\] |
| Answer» C. \[{{c}^{2}}={{b}^{2}}{{m}^{2}}-{{a}^{2}}\] | |
| 4331. |
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 |
| B. | ?1/a |
| C. | a |
| D. | ? a |
| Answer» C. a | |
| 4332. |
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. | \[a-b\] |
| B. | \[\sqrt{a-b}\] |
| C. | \[\sqrt{{{a}^{2}}-{{b}^{2}}}\] |
| D. | \[\sqrt{{{a}^{2}}+{{b}^{2}}}\] |
| Answer» D. \[\sqrt{{{a}^{2}}+{{b}^{2}}}\] | |
| 4333. |
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. | \[{{45}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{30}^{o}}\] |
| D. | \[{{75}^{o}}\] |
| Answer» D. \[{{75}^{o}}\] | |
| 4334. |
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. | \[{{a}^{2}}{{\cos }^{2}}\alpha +{{b}^{2}}{{\sin }^{2}}\alpha ={{p}^{2}}\] |
| B. | \[{{a}^{2}}{{\cos }^{2}}\alpha -{{b}^{2}}{{\sin }^{2}}\alpha ={{p}^{2}}\] |
| C. | \[{{a}^{2}}{{\sin }^{2}}\alpha +{{b}^{2}}{{\cos }^{2}}\alpha ={{p}^{2}}\] |
| D. | \[{{a}^{2}}{{\sin }^{2}}\alpha -{{b}^{2}}{{\cos }^{2}}\alpha ={{p}^{2}}\] |
| Answer» C. \[{{a}^{2}}{{\sin }^{2}}\alpha +{{b}^{2}}{{\cos }^{2}}\alpha ={{p}^{2}}\] | |
| 4335. |
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) |
| B. | (3, 4) |
| C. | (4, ?3) |
| D. | None of these |
| Answer» B. (3, 4) | |
| 4336. |
The equation of the tangent to the conic \[{{x}^{2}}-{{y}^{2}}-8x+2y+11=0\] at (2, 1) is [Karnataka CET 1993] |
| A. | \[x+2=0\] |
| B. | \[2x+1=0\] |
| C. | \[x-2=0\] |
| D. | \[x+y+1=0\] |
| Answer» D. \[x+y+1=0\] | |
| 4337. |
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. | \[\sqrt{\frac{17}{20}}\] |
| B. | \[\sqrt{\frac{20}{17}}\] |
| C. | \[\sqrt{\frac{3}{20}}\] |
| D. | \[\sqrt{\frac{20}{3}}\] |
| Answer» B. \[\sqrt{\frac{20}{17}}\] | |
| 4338. |
The one which does not represent a hyperbola is [MP PET 1992] |
| A. | \[xy=1\] |
| B. | \[{{x}^{2}}-{{y}^{2}}=5\] |
| C. | \[(x-1)(y-3)=3\] |
| D. | \[{{x}^{2}}-{{y}^{2}}=0\] |
| Answer» E. | |
| 4339. |
The equation of the tangent to the hyperbola \[4{{y}^{2}}={{x}^{2}}-1\] at the point (1, 0) is [Karnataka CET 1994] |
| A. | \[x=1\] |
| B. | \[y=1\] |
| C. | \[y=4\] |
| D. | \[x=4\] |
| Answer» B. \[y=1\] | |
| 4340. |
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. | \[{{m}_{1}}+{{m}_{2}}=\frac{24}{11}\] |
| B. | \[{{m}_{1}}{{m}_{2}}=\frac{20}{11}\] |
| C. | \[{{m}_{1}}+{{m}_{2}}=\frac{48}{11}\] |
| D. | \[{{m}_{1}}{{m}_{2}}=\frac{11}{20}\] |
| Answer» C. \[{{m}_{1}}+{{m}_{2}}=\frac{48}{11}\] | |
| 4341. |
The equation of the tangents to the hyperbola \[3{{x}^{2}}-4{{y}^{2}}=12\] which cuts equal intercepts from the axes, are |
| A. | \[y+x=\pm 1\] |
| B. | \[y-x=\pm 1\] |
| C. | \[3x+4y=\pm 1\] |
| D. | \[3x-4y=\pm 1\] |
| Answer» C. \[3x+4y=\pm 1\] | |
| 4342. |
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. | \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] |
| B. | \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] |
| C. | \[{{x}^{2}}+{{y}^{2}}=2ab\] |
| D. | None of these |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}=2ab\] | |
| 4343. |
The equation of the tangents to the conic \[3{{x}^{2}}-{{y}^{2}}=3\] perpendicular to the line \[x+3y=2\] is |
| A. | \[y=3x\pm \sqrt{6}\] |
| B. | \[y=6x\pm \sqrt{3}\] |
| C. | \[y=x\pm \sqrt{6}\] |
| D. | \[y=3x\pm 6\] |
| Answer» B. \[y=6x\pm \sqrt{3}\] | |
| 4344. |
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. | \[x{{\sec }^{2}}\theta -y{{\tan }^{2}}\theta =1\] |
| B. | \[\frac{x}{a}\sec \theta -\frac{y}{b}\tan \theta =1\] |
| C. | \[\frac{x+a\sec \theta }{{{a}^{2}}}-\frac{y+b\tan \theta }{{{b}^{2}}}=1\] |
| D. | None of these |
| Answer» C. \[\frac{x+a\sec \theta }{{{a}^{2}}}-\frac{y+b\tan \theta }{{{b}^{2}}}=1\] | |
| 4345. |
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) |
| B. | (2, 1/4) |
| C. | (1, 3) |
| D. | None of these |
| Answer» B. (2, 1/4) | |
| 4346. |
If the line \[y=2x+\lambda \] be a tangent to the hyperbola \[36{{x}^{2}}-25{{y}^{2}}=3600\], then \[\lambda =\] |
| A. | 16 |
| B. | ?16 |
| C. | \[\pm 16\] |
| D. | None of these |
| Answer» D. None of these | |
| 4347. |
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. | \[{{a}^{2}}{{l}^{2}}+{{b}^{2}}{{m}^{2}}={{n}^{2}}\] |
| B. | \[{{a}^{2}}{{l}^{2}}-{{b}^{2}}{{m}^{2}}={{n}^{2}}\] |
| C. | \[a{{m}^{2}}-{{b}^{2}}{{n}^{2}}={{a}^{2}}{{l}^{2}}\] |
| D. | None of these |
| Answer» C. \[a{{m}^{2}}-{{b}^{2}}{{n}^{2}}={{a}^{2}}{{l}^{2}}\] | |
| 4348. |
The eccentricity of a hyperbola passing through the points (3, 0), \[(3\sqrt{2},\ 2)\] will be [MNR 1985; UPSEAT 2000] |
| A. | \[\sqrt{13}\] |
| B. | \[\frac{\sqrt{13}}{3}\] |
| C. | \[\frac{\sqrt{13}}{4}\] |
| D. | \[\frac{\sqrt{13}}{2}\] |
| Answer» C. \[\frac{\sqrt{13}}{4}\] | |
| 4349. |
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) |
| B. | (5/2, 9/2) |
| C. | (?9/2, ?5/2) |
| D. | None of these |
| Answer» D. None of these | |
| 4350. |
The latus rectum of the hyperbola \[9{{x}^{2}}-16{{y}^{2}}+72x-32y-16=0\] is [Pb. CET 2004] |
| A. | \[\frac{9}{2}\] |
| B. | \[-\frac{9}{2}\] |
| C. | \[\frac{32}{3}\] |
| D. | \[-\frac{32}{3}\] |
| Answer» B. \[-\frac{9}{2}\] | |