Hyperbola - Coordinate Geometry - Mathematics Previous Year Questions

1

2016 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2016

If PQ is a double ordinate of the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\) such that \(\Delta OPQ\) is equilateral. O being the centre. Then, the eccentricity e satisfies

A

\(1 < e < {2 \over {\sqrt 3 }}\)

B

\(e = {2 \over {\sqrt 2 }}\)

C

\(e = {{\sqrt 3 } \over 2}\)

D

\(e > {2 \over {\sqrt 3 }}\)

Open complete paper

2

2017 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2017

The line segment joining the foci of the hyperbola \({x^2} - {y^2} + 1 = 0\) is one of the diameters of a circle. The equation of the circle is

A

\({x^2} + {y^2} = 4\)

B

\({x^2} + {y^2} = \sqrt 2\)

C

\({x^2} + {y^2} = 2\)

D

\({x^2} + {y^2} = 2\sqrt 2\)

Open complete paper

3

2017 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2017

Let A(\(-\) 1, 0) and B(2, 0) be two points. A point M moves in the plane in such a way that \(\angle MBA\) = 2\(\angle MAB\). Then, the point M moves along

A

a straight line

B

a parabola

C

an ellipse

D

a hyperbola

Open complete paper

4

2017 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2017

Let P be the foot of the perpendicular from focus S of hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\) on the line bx \(-\) ay = 0 and let C be the centre of the hyperbola. Then, the area of the rectangle whose sides are equal to that of SP and CP is

A

2ab

B

ab

C

\({{({a^2} + {b^2})} \over 2}\)

D

\({a \over b}\)

Open complete paper

5

2018 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2018

A hyperbola, having the transverse axis of length 2sin\(\theta\) is confocal wit6h the ellipse 3x² + 4y² = 12. Its equation is

A

x²sin²\(\theta\) \(-\) y²cos²\(\theta\) = 1

B

x²cosec²\(\theta\) \(-\) y²sec²\(\theta\) = 1

C

(x² + y²)sin²\(\theta\) = 1 + y²

D

x²cosec²\(\theta\) = x² + y² + sin²\(\theta\)

Open complete paper

6

2018 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2018

Let the eccentricity of the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\) be reciprocal to that of the ellipse x² + 9y² = 9, then the ratio of a² : b² equals to

A

8 : 1

B

1 : 8

C

9 : 1

D

1 : 9

Open complete paper

7

2019 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2019

For the hyperbola \({{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1\), which of the following remains fixed when \(\alpha\) varies?

A

directrix

B

vertices

C

foci

D

eccentricity

Open complete paper

8

2019 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2019

The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is

A

\(= \sqrt 2\)

B

\(> \sqrt 2\)

C

\(< \sqrt 2\)

D

\(< {1 \over {\sqrt 2 }}\)

Open complete paper

9

2019 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2019

Let P(4, 3) be a point on the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\). If the normal at P intersects the X-axis at (16, 0), then the eccentricity of the hyperbola is

A

\({{\sqrt 5 } \over 2}\)

B

2

C

\({\sqrt 2 }\)

D

\({\sqrt 3 }\)

Open complete paper

10

2019 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2019

The equation of the directrices of the hyperbola \(3{x^2} - 3{y^2} - 18x + 12y + 2 = 0\) is

A

\(x = 3 \pm \sqrt {{{13} \over 6}}\)

B

\(x = 3 \pm \sqrt {{{6} \over 13}}\)

C

\(x = 6 \pm \sqrt {{{13} \over 3}}\)

D

\(x = 6 \pm \sqrt {{{3} \over 13}}\)

Open complete paper

11

2019 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2019

Equation of a tangent to the hyperbola 5x² \(-\) y² = 5 and which passes through an external point (2, 8) is

A

3x \(-\) y + 2 = 0

B

3x + y \(-\) 14 = 0

C

23x \(-\) 3y \(-\) 22 = 0

D

3x \(-\) 23y + 178 = 0

Open complete paper

12

2019 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2019

A point is in motion along a hyperbola \(y = {{10} \over x}\) so that its abscissa x increases uniformly at a rate of 1 unit per second. Then, the rate of change of its ordinate when the point passes through (5, 2)

A

increases at the rate of \({1 \over 2}\) unit per second

B

decreases at the rate of \({1 \over 2}\) unit per second

C

decreases at the rate of \({2 \over 5}\) unit per second

D

increases at the rate of \({2 \over 5}\) unit per second

Open complete paper

13

2020 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2020

A double ordinate PQ of the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\) is such that \(\Delta OPQ\) is equilateral, O being the centre of the hyperbola. Then the eccentricity e satisfies the relation

A

\(1 < e < {2 \over {\sqrt 3 }}\)

B

\(e = {2 \over {\sqrt 3 }}\)

C

\(e = {{\sqrt 3 } \over 2}\)

D

\(e > {2 \over {\sqrt 3 }}\)

Open complete paper

14

2021 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2021

The locus of the centre of a variable circle which always touches two given circles externally is

A

an ellipse

B

a hyperbola

C

a parabola

D

a circle

Open complete paper

15

2021 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2021

The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G from the origin is twice the abscissa of P then the curve is

A

a parabola

B

a circle

C

a hyperbola

D

an ellipse

Open complete paper

16

2022 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2022

Let \(P(3\sec \theta ,2\tan \theta )\) and \(Q(3\sec \phi ,2\tan \phi )\) be two points on \({{{x^2}} \over 9} - {{{y^2}} \over 4} = 1\) such that \(\theta + \phi = {\pi \over 2},0 < \theta ,\phi < {\pi \over 2}\). Then the ordinate of the point of intersection of the normals at P and Q is

A

\({{13} \over 2}\)

B

\(- {{13} \over 2}\)

C

\({5 \over 2}\)

D

\(- {5 \over 2}\)

Open complete paper

17

2022 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2022

The line y = x + 5 touches

A

the parabola y² = 20 x

B

the ellipse \(9{x^2} + 16{y^2} = 144\)

C

the hyperbola \({{{x^2}} \over {29}} - {{{y^2}} \over 4} = 1\)

D

the circle \({x^2} + {y^2} = 25\)

Open complete paper

18

2022 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2022

PQ is a double ordinate of the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\) such that \(\Delta OPQ\) is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies

A

\(1 < e < {2 \over {\sqrt 3 }}\)

B

\(e = {2 \over {\sqrt 3 }}\)

C

\(e = 2\sqrt 3\)

D

\(e > {2 \over {\sqrt 3 }}\)

Open complete paper

19

2023 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2023

If a hyperbola passes through the point P(\(\sqrt2\), \(\sqrt3\)) and has foci at (\(\pm\) 2, 0), then the tangent to this hyperbola at P is

A

\(y = x\sqrt 6 - \sqrt 3\)

B

\(y = x\sqrt 3 - \sqrt 6\)

C

\(y = x\sqrt 6 + \sqrt 3\)

D

\(y = x\sqrt 3 + \sqrt 6\)

Open complete paper

20

2023 · Mathematics · Coordinate Geometry · Hyperbola

WB JEE 2023

The average length of all vertical chords of the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1,a \le x \le 2a\), is :

A

\(b\{ 2\sqrt 3 - \ln (2 + \sqrt 3 )\}\)

B

\(b\{ 3\sqrt 2 + \ln (3 + \sqrt 2 )\}\)

C

\(a\{ 2\sqrt 5 - \ln (2 + \sqrt 5 )\}\)

D

\(a\{ 5\sqrt 2 + \ln (5 + \sqrt 2 )\}\)

Open complete paper