Beta Question Bank for Engineering: Mathematics>Chapter 20 - Hyperbola>EXERCISE-4>Q 19

HARD

JEE Main/Advance

IMPORTANT

Earn 100

A tangent to the parabola $x^{2} = 4 a y$ meets the hyperbola $x y = k^{2}$ in two points $P$ and $Q$ . Prove that the middle point of $P Q$ lies on the parabola.

Important Questions on Hyperbola

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 20 - Hyperbola>EXERCISE-1>Q 5

The equation of the hyperbola whose foci are

(6, 5), (- 4, 5)

and eccentricity is

\frac{5}{4}

, is

MEDIUM

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 20 - Hyperbola>EXERCISE-2>Q 8

The tangent to the hyperbola.

x^{2} - 3 y^{2} = 3

at the point

(\sqrt{3}, 0)

when associated with two asymptotes constitutes-

EASY

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 20 - Hyperbola>EXERCISE-2>Q 13

If

(5, 12)

and

(24, 7)

are the focii of a conic passing through the origin, then the eccentricity of conic is-

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 20 - Hyperbola>EXERCISE-2>Q 17

If the normal at point

P

to the rectangular hyperbola

x^{2} - y^{2} = 4

meets the transverse and conjugate axes at

A

and

B

respectively and

C

is centre of the hyperbola, then-

MEDIUM

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 20 - Hyperbola>EXERCISE-2>Q 18

If the circle

x^{2} + y^{2} = a^{2}

intersects the hyperbola

x y = c^{2}

in four points

P (x_{1}, y_{2}), Q (x_{2}, y_{2}), R (x_{3}, y_{3}), S (x_{4}, y_{4}),

then

MEDIUM

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 20 - Hyperbola>EXERCISE-2>Q 20

Consider the hyperbola

3 x^{2} - y^{2} - 24 x + 4 y - 4 = 0

-

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 20 - Hyperbola>EXERCISE-2>Q 23

The equation of common tangent of hyperbola

9 x^{2} - 9 y^{2} = 8

and the parabola

y^{2} = 32 x

is/are -

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 20 - Hyperbola>EXERCISE-4>Q 20

Given the base of a triangle and the ratio of the tangent of half the base angles. Show that the vertex moves on a hyperbola whose foci are the extremities of the base.