Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 11 - Straight Lines>EXERCISES 11 (b)>Q 31

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11th Odisha Board

IMPORTANT

Earn 100

Find the acute angle between the pair of lines given by: $x^{2} + 2 x y - 4 y^{2} = 0$ .

Important Questions on Straight Lines

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 11 - Straight Lines>EXERCISES 11 (b)>Q 31

Find the acute angle between the pair of lines given by:

2 x^{2} + x y - 3 y^{2} + 3 x + 2 y + 1 = 0

.

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 11 - Straight Lines>EXERCISES 11 (b)>Q 31

Find the acute angle between the pair of lines given by:

x^{2} + x y - 6 y^{2} - x - 8 y - 2 = 0

.

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 11 - Straight Lines>EXERCISES 11 (b)>Q 32

Write down the equation of the pair of bisectors of the following pair of lines:

x^{2} - y^{2} = 0

.

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 11 - Straight Lines>EXERCISES 11 (b)>Q 32

Write down the equation of the pair of bisectors of the following pair of lines:

4 x^{2} - x y - 3 y^{2} = 0

.

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 11 - Straight Lines>EXERCISES 11 (b)>Q 32

Write down the equation of the pair of bisectors of the following pair of lines:

x^{2} \cos θ + 2 x y - y^{2} \sin θ = 0

.

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 11 - Straight Lines>EXERCISES 11 (b)>Q 32

Write down the equation of the pair of bisectors of the following pair of lines:

x^{2} - 2 x y \tan θ - y^{2} = 0

.

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 11 - Straight Lines>EXERCISES 11 (b)>Q 33

If the pair of lines represented

x^{2} - 2 p x y - y^{2} = 0 and x^{2} - 2 q x y - y^{2} = 0

be such that each pair bisects the angle between the other pair, then prove that

p q = - 1

.

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 11 - Straight Lines>EXERCISES 11 (b)>Q 34

Transform the equation

x^{2} + y^{2} - 2 x - 4 y + 1 = 0

by shifting the origin to

(1, 2)

and keeping the axes parallel.