Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 32

MEDIUM

JEE Advanced

IMPORTANT

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Two concentric hyperbolas, whose axes meet at angle of $45^{°}$ , cut

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Important Questions on Hyperbola

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 33

The number of triangles which can be inscribed in the rectangular hyperbola

x y = c^{2}

and whose all sides touch the parabola

y^{2} = 4 a x

, is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 34

If

(x - 1) (y - 2) = 5

and

{(x - 1)}^{2} + {(y + 2)}^{2} = r^{2}

intersect at four points

A, B, C, D

and centroid of

Δ A B C

lies on line

y = 3 x - 4

, then locus of

D

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 35

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

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

is

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