Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.3>Q 2

EASY

JEE Main/Advanced

IMPORTANT

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If co-ordinate axes are the angle bisectors of the pair of lines $a x^{2} + 2 h x y + b y^{2} = 0$ then:

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Important Questions on Pair of Straight Lines

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.3>Q 3

If the line

y = m x

is one of the bisector of the lines

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

, then the value of

m =

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.3>Q 4

If one of the lines of

m y^{2} + (1 - m^{2}) x y - m x^{2} = 0

is a bisector of the angle between the lines

x y = 0,

then

m

is

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.3>Q 5

The bisectors of the angles between the lines

{(a x + b y)}^{2} = c {(b x - a y)}^{2}, c > 0

are respectively parallel and perpendicular to the line :

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.3>Q 1

If the pairs of straight lines

a x^{2} + 2 h x y - a y^{2} = 0

and

b x^{2} + 2 g x y - b y^{2} = 0

be such that each bisects the angles between the other, then prove that

h g + a b = 0

.

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.3>Q 2

Prove that the lines

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

and

4 x^{2} + 18 x y + y^{2} = 0

. are equally inclined to the lines

b = 1

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.3>Q 3

Show that the lines bisecting the angle between the bisectors of the angles between the lines

a x^{2} + 2 h x y + b y^{2} = 0

are given by

(a - b) (x^{2} - y^{2}) + 4 h x y = 0

.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.3>Q 4

Prove that the bisectors of the angle between the lines

a x^{2} + a c x y + c y^{2} = 0

and

(3 + \frac{1}{c}) x^{2} + x y + (3 + \frac{1}{a}) y^{2} = 0

are always the same.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.3>Q 5

The lines represented by

x^{2} + 2 λ x y + 2 y^{2} = 0

and the lines represented by

(1 + λ) x^{2} - 8 x y + y^{2} = 0

are equally inclined, then find the values of

λ

.