Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>INTRODUCTORY EXERCISE 7.1>Q 5

MEDIUM

JEE Main/Advanced

IMPORTANT

Earn 100

Find the eccentricity of the conjugate hyperbola $x^{2} - 3 y^{2} = 1$ .

Important Questions on Hyperbola

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>INTRODUCTORY EXERCISE 7.1>Q 6

For what value of

λ,

does the line

y = 3 x + λ

touch the hyperbola

9 x^{2} - 5 y^{2} = 45 ?

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>INTRODUCTORY EXERCISE 7.1>Q 7

Find the equation of tangent to the parabola

y^{2} = 16 x

which is parallel to the line

3 x - 4 y + 5 = 0

. Also find the point of contact.

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>INTRODUCTORY EXERCISE 7.2>Q 1

A common tangent to

9 x^{2} - 16 y^{2} = 144

and

x^{2} + y^{2} = 9

, is

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>INTRODUCTORY EXERCISE 7.2>Q 2

The tangents from

(1, 2 \sqrt{2})

to the hyperbola

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

include between them an angle equal to

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>INTRODUCTORY EXERCISE 7.2>Q 3

The tangent at a point

P

on the hyperbola

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

passes through the point

(0, - b)

and the normal at

P

passes through the point

(2 a \sqrt{2}, 0)

. Then the eccentricity of the hyperbola is

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>INTRODUCTORY EXERCISE 7.2>Q 4

The equation of the chord of hyperbola

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

whose mid-point is

(5, 3)

, is

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>INTRODUCTORY EXERCISE 7.2>Q 5

The value of

m

for which

y = m x + 6

is a tangent to the hyperbola

\frac{x^{2}}{100} - \frac{y^{2}}{49} = 1

is

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>INTRODUCTORY EXERCISE 7.2>Q 6

P

is a point on the hyperbola

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

is the foot of the perpendicular from

P

on the transverse axis. The tangent to the hyperbola at

P

meets the transverse axis at

T

. If

O

is the centre of the hyperbola, then

O T \cdot O N

is equal to