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The eccentricity of the hyperbola whose length of its conjugate axis is equal to half of the distance between its foci, is

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Important Questions on Hyperbola

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 10th April 2016>Q 32

A hyperbola whose transverse axis is along the major axis of the conic

\frac{x^{2}}{3} + \frac{y^{2}}{4} = 4

and has vertices at the foci of the conic. If the eccentricity of the hyperbola is

\frac{3}{2}

, then which of the following points does not lie on the hyperbola

?

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 19th April 2014>Q 33

The tangent at an extremity (in the first quadrant) of the latus rectum of the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{5} = 1$ , meets the $x$ -axis and $y$ -axis at $A$ and $B$ , respectively. Then $O A^{2} - O B^{2}$ , where $O$ is the origin, equals

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 24 June 2022 Shift 1>Q 34

Let

λ x - 2 y = μ

be a tangent to the hyperbola

a^{2} x^{2} - y^{2} = b^{2}

. Then

{(\frac{λ}{a})}^{2} - {(\frac{μ}{b})}^{2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 25 June 2022 Shift 2>Q 35

Let the eccentricity of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

\frac{5}{4}

. If the equation of the normal at the point

(\frac{8}{\sqrt{5}}, \frac{12}{5})

on the hyperbola is

8 \sqrt{5} x + β y = λ

, then

λ - β

is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 26 June 2022 Shift 2>Q 36

The normal to the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{9} = 1

at the point

(8, 3 \sqrt{3})

on it, passes through the point

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 26 June 2022 Shift 2>Q 37

Let a line

L_{1}

be tangent to the hyperbola

\frac{x^{2}}{16} - \frac{y^{2}}{4} = 1

and let

L_{2}

be the line passing through the origin and perpendicular to

L_{1}

. If the locus of the point of intersection of

L_{1}

and

L_{2}

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

α x^{2} + β y^{2}

, then

α + β

is equal to ______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 28 June 2022 Shift 1>Q 38

Let the eccentricity of the hyperbola

H : \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

\sqrt{\frac{5}{2}}

and length of its latus rectum be

6 \sqrt{2}

. If

y = 2 x + c

is a tangent to the hyperbola

H

, then the value of

c^{2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 28 June 2022 Shift 2>Q 39

Let

a > 0, b > 0

. Let

e

and

l

respectively be the eccentricity and length of the latus rectum of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

. Let

e^{'}

and

l^{'}

respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If

e^{2} = \frac{11}{14} l

and

{(e^{'})}^{2} = \frac{11}{8} l^{'}

, then the value of

77 a + 44 b

is equal to

The eccentricity of the hyperbola whose length of its conjugate axis is equal to half of the distance between its foci, is

Important Questions on Hyperbola

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