Mathematics Crash Course JEE Advanced>Chapter 11 - Hyperbola>Exercise 1>Q 13

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IMPORTANT

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If $2 x - y + 1 = 0$ is a tangent to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{16} = 1$ then which of the following CANNOT be sides of a right angled triangle?

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Important Questions on Hyperbola

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 11 - Hyperbola>Exercise 1>Q 14

The normal to the hyperbola

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

meets the axes in

M

and

N

, and lines

M P

and

N P

are drawn at right angle to the axes then locus of

P

is a hyperbola with eccentricity

e'

, if eccentricity of

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

is

e

then

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Mathematics Crash Course JEE Advanced>Chapter 11 - Hyperbola>Exercise 1>Q 15

If the axis of a varying central hyperbola

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

be fixed in magnitude and position, then locus of point of contact of a tangent drawn to it from a fixed point on

x

-axis is

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 11 - Hyperbola>Exercise 1>Q 16

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

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

from

(α, α^{2}),

then

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Mathematics Crash Course JEE Advanced>Chapter 11 - Hyperbola>Exercise 1>Q 17

Three points

A, B

and

C

are taken on a rectangular hyperbola

x y = 4

, where

B

and

C

have co-ordinates

(- 2, - 2)

and

(6, \frac{2}{3})

respectively and

A

lies in the first quadrant. If the normal at

A

is parallel to

B C

, then

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IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 11 - Hyperbola>Exercise 1>Q 19

A square

A B C D

has all its vertices on the curve

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

The midpoints of its sides also lie on the same curve. Then, the square of area of

A B C D

is