Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>INTRODUCTORY EXERCISE 2.4>Q 6

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The equation of the bisector of that angle between the lines $x + y = 3$ and $2 x - y = 2$ which contains the point $(1, 1)$ is :

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Important Questions on The Straight Lines

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>INTRODUCTORY EXERCISE 2.4>Q 1

Find the equations of the straight lines passing through

(2, - 1)

and making an angle of

45 °

with the line

6 x + 5 y - 8 = 0

.

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>INTRODUCTORY EXERCISE 2.4>Q 2

Equation of the base of an equilateral triangle is

3 x + 4 y = 9

and its vertex is at the point

(1, 2)

. Find the equations of the other sides and the length of each side of the triangle.

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>INTRODUCTORY EXERCISE 2.4>Q 3

Find the co-ordinates of those points on the line

3 x + 2 y = 5

which are equidistant from the lines

4 x + 3 y - 7 = 0

and

2 y - 5 = 0

.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>INTRODUCTORY EXERCISE 2.4>Q 4

Two sides of a rhombus

A B C D

are parallel to the lines

y = x + 2

and

y = 7 x + 3

. If the diagonals of the rhombus intersect at the point

(1, 2)

and the vertex

A

is on the

y

-axis, then find the possible coordinates of

A

.

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>INTRODUCTORY EXERCISE 2.4>Q 5

The bisector of two lines

L_{1}

and

L_{2}

are given by

3 x^{2} - 8 x y - 3 y^{2} + 10 x + 20 y - 25 = 0

. If the line

L_{1}

passes through origin, find the equation of line

L_{2}

.

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>INTRODUCTORY EXERCISE 2.4>Q 6

Find the equation of the bisector of the angle between the lines

x + 2 y - 11 = 0

and

3 x - 6 y - 5 = 0

which contains the point

(1, - 3)

.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>INTRODUCTORY EXERCISE 2.4>Q 7

Find the equation of the bisector of the angle between the lines

2 x - 3 y - 5 = 0

and

6 x - 4 y + 7 = 0

, which contains the point

(2, - 1)

.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>INTRODUCTORY EXERCISE 2.5>Q 1

The image of the point

(4, - 3)

with respect to the line

y = x

is :