EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Hyperbola>WBJEE 2019>Q 2

MEDIUM

WBJEE

IMPORTANT

Earn 100

For the hyperbola $\frac{x^{2}}{\cos^{2} α} - \frac{y^{2}}{\sin^{2} α} = 1,$ which of the following remains fixed when $α$ varies?

50% studentsanswered this correctly

Important Questions on Hyperbola

MEDIUM

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Hyperbola>WBJEE 2019>Q 3

The equation of the directrices of the hyperbola

3 x^{2} - 3 y^{2} - 18 x + 12 y + 2 = 0

is

EASY

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Hyperbola>WBJEE 2019>Q 4

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

e

is

EASY

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Hyperbola>WBJEE 2018>Q 5

Let the eccentricity of the hyperbola

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

be reciprocal to that of the ellipse

x^{2} + 9 y^{2} = 9,

then the ratio

a^{2} : b^{2}

equals

HARD

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Hyperbola>WBJEE 2018>Q 6

A hyperbola, having the transverse axis of length

2 \sin θ

is confocal with the ellipse

3 x^{2} + 4 y^{2} = 12 .

Its equation is

HARD

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Hyperbola>WBJEE 2019>Q 7

Let

P (4, 3)

be a point on the hyperbola

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

If the normal at

P

intersects the

X -

axis at

(16, 0),

then the eccentricity of the hyperbola is

HARD

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Hyperbola>WBJEE 2019>Q 8

Equation of a tangent to the hyperbola

5 x^{2} - y^{2} = 5

and which passes through an external point

(2, 8)

is