Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 4

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For the hyperbola $x y = 8$ , any tangent of it at $P$ meets co-ordinate axes at $Q$ and $R$ . Then area of triangle $C Q R$ where $C$ is center of the hyperbola, is

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Important Questions on Hyperbola

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 5

The tangent and normal at a point on

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

cuts the

y

-axis at

A

and

B

. Then the circle drawn on

A B

as diameter passes through

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 6

If

4 x^{2} + p y^{2} = 45

and

x^{2} - 4 y^{2} = 5

cut orthogonally, then the value of

p

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 7

A tangent drawn to hyperbola

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

at

P (\frac{π}{6})

forms a triangle of area

3 a^{2}

square units with coordinate axes, then the square of its eccentricity is equal to

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 8

If

m

is the slope of a tangent to the hyperbola

\frac{x^{2}}{a^{2} - b^{2}} - \frac{y^{2}}{a^{3} - b^{3}} = 1

, where

a > b > 1

, then

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 9

Two tangents to the hyperbola

\frac{x^{2}}{25} - \frac{y^{2}}{9} = 1

having slopes

2

and

m

where

(m \neq 2)

cuts the axes at four concyclic points. Then the slope

m

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 10

The equation of the chord of hyperbola

25 x^{2} - 16 y^{2} = 400

whose mid-point is

(5, 3)

, is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 11

If a chord joining

P (a \sec θ, a \tan θ)

and

Q (a \sec α, a \tan α)

on the hyperbola

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

is the normal at

P

, then

\tan α

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 12

The number of normal(s) of a rectangular hyperbola that can touch its conjugate is equal to