Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 32

HARD

Mathematics

IMPORTANT

Earn 100

Tangents are drawn to the hyperbola $4 x^{2} - y^{2} = 36$ at the points $P$ and $Q$ . If these tangents intersect at the point $T (0, 3)$ , then the area (in sq. units) of $△ P T Q$ is

100% studentsanswered this correctly

Important Questions on Hyperbola

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 33

The foot of perpendicular drawn from the focus to any tangent of the hyperbola lies on

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 34

If the focus of a hyperbola is

(\pm 3, 0)

and the equation of a tangent is

2 x + y - 4 = 0

, then the equation of the hyperbola is

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 35

Equation of the straight line(s) which touch(es) the hyperbola

x^{2} - y^{2} = \frac{8}{9}

and parabola

y^{2} = 32 x

is(are)

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 36

A line parallel to the straight line

2 x - y = 0

is tangent to the hyperbola

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

at the point

(x_{1}, y_{1})

. Then

x_{1}^{2} + 5 y_{1}^{2}

is equal to

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 37

If the line

y = m x + c

is a common tangent to the hyperbola

\frac{x^{2}}{100} - \frac{y^{2}}{64} = 1

and the circle

x^{2} + y^{2} = 36,

then which one of the following is true?

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 38

If the tangents drawn to the hyperbola

4 y^{2} = x^{2} + 1

intersect the co-ordinate axes at the distinct points

A

and

B

, then the locus of the mid point of

A B

is :

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 39

The equation of the common tangents to the two hyperbola

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

and

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

are:

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 40

Let

P

be the point of intersection of the common tangents to the parabola

y^{2} = 12 x

and the hyperbola

8 x^{2} - y^{2} = 8

. If

S

and

S^{'}

denote the foci of the hyperbola where

S

lies on the positive

x

-axis then

P

divides

S S^{'}

in a ratio: