Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.9>Q 18

MEDIUM

JEE Main

IMPORTANT

Earn 100

Find the equations of the lines through the point of intersection of the lines $x - 3 y + 1 = 0$ and $2 x + 5 y - 9 = 0$ and whose distance from the origin is $\sqrt{5}$ .

Important Questions on Straight Lines

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.9>Q 19

Find the equations of the lines through the point of intersection of the lines

x - y + 1 = 0

and

2 x - 3 y + 5 = 0

and whose distance from the point

(3, 2)

is

\frac{7}{5}

.

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.9>Q 20

If the length of the perpendicular from the point

(1, 1)

to the line

a x - b y + c = 0

be unity, show that

\frac{1}{c} + \frac{1}{a} - \frac{1}{b} = \frac{c}{2 a b}

.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.9>Q 21

Find the length of the perpendicular from the origin to the line joining two points whose coordinates are

(\cos θ, \sin θ)

and

(\cos ϕ, \sin ϕ)

.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.9>Q 22

If

p

and

p_{1}

be the lengths of the perpendiculars drawn from the origin upon the straight lines

x \sin θ + y \cos θ = \frac{1}{2} a \sin 2 θ

and

x \cos θ - y \sin θ = a \cos 2 θ

, prove that

4 p^{2} + p_{1}^{2} = a^{2}

.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.9>Q 23

Prove that the perpendicular distance between the lines

4 x + 3 y = 11

and

8 x + 6 y = 15

is

\frac{7}{10}

.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.9>Q 23

Find the distance between the pairs of lines:

3 x - 4 y + 5 = 0

and

3 x - 4 y + 7 = 0

.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.9>Q 24

If sum of the perpendicular distances of a variable point

P (x, y)

from the lines

x + y - 5 = 0

and

3 x - 2 y + 7 = 0

is always

10 .

Show that

P

must move on a line.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.9>Q 25

Determine the distance between the following pair of parallel lines:

$4 x - 3 y - 9 = 0$ and $4 x - 3 y - 24 = 0$