MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.10>Q 7

EASY

11th CBSE

IMPORTANT

Earn 100

Classify the following pair of lines as coincident, parallel or intersecting: $x - y = 0 and 3 x - 3 y + 5 = 0$

Important Questions on The Straight Lines

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.10>Q 8

Find the equation of the line joining the point

(3, 5)

to the point of intersection of the lines

4 x + y - 1 = 0

and

7 x - 3 y - 35 = 0

.

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.10>Q 9

Find the equation of the line passing through the point of intersection of the lines

4 x - 7 y - 3 = 0

and

2 x - 3 y + 1 = 0

that has equal intercepts on the axes.

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.10>Q 10

Show that the area of the triangle formed by the lines

y = m_{1} x, y = m_{2} x

and

y = c

is equal to

\frac{c^{2}}{4} (\sqrt{33} + \sqrt{11})

, where

m_{1}, m_{2}

are the roots of the equation

x^{2} + (\sqrt{3} + 2) x + \sqrt{3} - 1 = 0

.

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.10>Q 11

If the straight line

\frac{x}{a} + \frac{y}{b} = 1

passes through the point of intersection of the lines

x + y = 3

and

2 x - 3 y = 1

and is parallel to

x - y - 6 = 0

, find

a

and

b

.

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.10>Q 12

Find the orthocentre of the triangle the equations of whose sides are

x + y = 1, 2 x + 3 y = 6

and

4 x - y + 4 = 0

.

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.10>Q 13

Three sides

A B, B C

and

C A

of a triangle

A B C

are

5 x - 3 y + 2 = 0, x - 3 y - 2 = 0

and

x + y - 6 = 0

respectively. Find the equation of the altitude through the vertex

A

.

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.10>Q 14

Find the coordinates of the orthocentre of the triangle whose vertices are

(- 1, 3), (2, - 1)

and

(0, 0)

.

HARD

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.10>Q 15

Find the coordinates of the incentre and centroid of the triangle whose sides have the equations

3 x - 4 y = 0, 12 y + 5 x = 0

and

y - 15 = 0

.