Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-2>Q 20

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Which of the following equations in parametric form can represent a hyperbolic profile, where $' t'$ is a parameter.

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Important Questions on Hyperbola

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-2>Q 21

If two distinct tangents can be drawn from the point

(α, 2)

on different branches of the hyperbola

\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1

, then the range of

α

is subset of

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-2>Q 22

A rectangular hyperbola whose centre is

C

is cut by any circle of radius

r

in four points

P, Q, R

and

S

. Then

C P^{2} + C Q^{2} + C R^{2} + C S^{2} =

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-2>Q 23

x^{2} + y^{2} = 16

is the auxilliary circle of

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-2>Q 24

If the chord joining the points whose eccentric angles are

α

and

β

on the hyperbola

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

is a focal chord, then

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-2>Q 25

If the normal at

P

to the rectangular hyperbola

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

meets the axes in

G

and

g

and

C

is the centre of the hyperbola, then

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-2>Q 26

Circles are drawn on chords of rectangular hyperbola

x y = c^{2}

parallel to the line

y = x

as diameters. All such circles pass through two fixed points whose co-ordinates are

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-2>Q 27

If a circle and the rectangular hyperbola

x y = c^{2}

meet in the four points

t_{1}, t_{2}, t_{3} & t_{4}

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-3>Q 1

An ellipse intersects the hyperbola

2 x^{2} - 2 y^{2} = 1

orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then