A variable chord of the hyperbola x 2 a 2 - y 2 b 2 = 1 b > a subtends a right angle at the centre of the hyperbola, then this chord touches

a fixed circle concentric with the hyperbola

a fixed ellipse concentric with the hyperbola

a fixed hyperbola concentric with the hyperbola

a fixed parabola having vertex at 0 , 0

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JEE Advanced

IMPORTANT

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If foci of hyperbola lie on $y = x$ and one of the asymptotes is $y = 2 x$ , then equation of the hyperbola, given that it passes through $(3, 4)$ , is

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Important Questions on Hyperbola

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 36

The exhaustive set of values of

α^{2}

such that there exists a tangent to the ellipse

x^{2} + α^{2} y^{2} = α^{2}

such that the portion of the tangent intercepted by the hyperbola

α^{2} x^{2} - y^{2} = 1

subtends a right angle at the centre of the curves, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 37

The locus of the point which is such that the chord of contact of tangents drawn from it to the ellipse

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

forms a triangle of constant area with the coordinate axes, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 38

The combined equation of the asymptotes of the hyperbola

2 x^{2} + 5 x y + 2 y^{2} + 4 x + 5 y = 0

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 39

From any point on the hyperbola

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

tangents are drawn to the hyperbola

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

. Then, area cut-off by the chord of contact on the asymptotes is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 40

A variable chord of the hyperbola

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

(b > a)

subtends a right angle at the centre of the hyperbola, then this chord touches

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 41

If two tangents can be drawn to the different branches of hyperbola

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

from the paint

(α, α^{2})

, then

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 42

If tangents

O Q

and

O R

are drawn to variable circles having radius

r

and the centre lying on the rectangular hyperbola

x y = 1

, then locus of circumcentre of

Δ O Q R

is (

O

being the origin)

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 43

Four points are such that the line joining any two points is perpendicular to the line joining other two points. If three points out of these lie on a rectangular hyperbola, then the fourth point will lie on

If foci of hyperbola lie on y=x and one of the asymptotes is y=2x, then equation of the hyperbola, given that it passes through 3,4, is

Important Questions on Hyperbola

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If foci of hyperbola lie on $y = x$ and one of the asymptotes is $y = 2 x$ , then equation of the hyperbola, given that it passes through $(3, 4)$ , is