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 , 2 3 respectively and A lies in the first quadrant. If the normal at A is parallel to B C , then

Orthocenter of ∆ A B C is 2 3 , 2 3

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

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Important Questions on Hyperbola

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 13

If the normal at a point

P

to the hyperbola meets the transverse axis at

G

and the value of

\frac{SG}{SP}

6

, then the eccentricity of the hyperbola is (where

S

is the focus of hyperbola)

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 14

If the normal to the hyperbola

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

at any point

P (a \sec θ, b \tan θ)

meets the transverse and conjugate axes in

G

and

g

, respectively, then value

P G

is greater than

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 15

If normal to the hyperbola

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

drawn at an extremity of its latus rectum has slope equal to slope of line which meets hyperbola only once, then the eccentricity of hyperbola is

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 16

At the point of intersection of the rectangular hyperbola

x y = c^{2}

and the parabola

y^{2} = 4 a x

, tangents to the rectangular hyperbola and the parabola make an angle

θ

and

ϕ

, respectively with the

x

-axis, then

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IMPORTANT

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

HARD

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 18

A tangent is drawn at any point on the hyperbola

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

. If this tangent is intersected by the tangents at the vertices at points

P

and

Q

, then which of the following is/are true? (Where

S, S^{'}

are foci of hyperbola.)

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JEE Main

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 1

The number of points from where a pair of perpendicular tangents can be drawn to the hyperbola

x^{2} \sec^{2} α - y^{2} {cosec}^{2} α = 1

α \in (0, \frac{π}{4})

, is

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 2

e

is the eccentricity of the hyperbola

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

and

θ

is the angle between the asymptotes, then

\cos \frac{θ}{2}

is equal to

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

Important Questions on Hyperbola

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