KC Sinha Mathematics Solution Class 11 Chapter 21 Straight Lines Exercise 21.3

Exercise 21.3

Page no 21.30

Type 1

Question 1

Find the equation of the line with slope 3 and y intercept -2

Question 2

(i) Find the equation of the line which cuts off an intercept 7 on y-axis and has the slope 3.

Question 3

Find the equation of the straight lines which cut off an intercept 4 from the

$y$ -axis and are equally inclined to the axes.

Question 4

Find the equation of the straight line which cuts off an intercept

$-5$ from the

$y$ -axis and makes an angle

$\theta$ with the

$x$ -axis such that

$\sin \theta=\frac{12}{13}$ and

$0<\theta<\frac{\pi}{2}$

Question 5

Find the equation of the line which intercepts a length 2 on the positive direction of the

$x$ -axis and is inclined at

$135^{\circ}$ with the positive direction of y-axis.

Question 6

(i) Find the equation of a line which cuts off an intercept 4 on the

$x$ -axis and has the slope

$2 .$

(ii) Write the equation of the lines for which

$\tan \theta=\frac{1}{2}$ , where

$\theta$ is the inclination of the line and (a)

$y$ -intercept

$-\frac{3}{2}(b) x$ -intercept 4 .

Question 7

(i) The perpendicular from the origin to the line

$y=m x+c$ meets it at the point

$(-1,2)$ . Find the values of

$m$ and

$c$ .

(ii) The line through the points

$(h, 3)$ and

$(4,1)$ intersects the line

$7 x-9 y-19=0$ at right angle. Find the value of

$h$ .

(iii) Find the values of

$k$ for which the line

$(k-3) x-\left(4-k^{2}\right) y+k^{2}-7 k+6=0$ is :

(a) parallel to the

$x$ -axis.

(b) parallel to the

$y$ -axis.

Type 2

Question 8

Find the equation of a line through the origin which makes an angle of

$45^{\circ}$ with the positive direction of

$x$ -axis.

Question 9

(i) Find the equation of the line through the point

$(-1,2)$ and having slope 4 .

(ii) Find the equation of the line through

$(-2,3)$ and having slope

$-4$ .

(iii) Find the equation of the line passing through

$(0,0)$ with slope

$m$ -

(iv) Find the equation of the line passing through

$(-4,3)$ and having slope

$\frac{1}{2}$

Page no 21.31

(v) Find the equation of the line intersecting

$x$ -axis at a distance of 3 units to the left of the origin and having slope

$-2$ .

(vi) Find the equation of the line passing through

$(2,2 \sqrt{3})$ and inclined with the

$x$ -axis at an angle of

$75^{\circ}$ .

Question 10

Find the equation of the line passing through the point

$(2,2)$ and inclined to x -axis at

$45^{\circ}$

Question 11

Find the equation of the line passing through the point (-1,-2) and having slope

$\frac{4}{7}$

Question 12

Find the equation of the line passing through the point

$(\sqrt{2}, 2 \sqrt{2})$ and having supe

$\frac{2}{3}$

Question 13

Find the equation of the line intersecting

$x$ -axis at a distance of 3 units to the left of the origin with slope

$-2$ .

Question 14

Find the equation of a line which passes through the point

$(-2,3)$ and makes an angle of

$60^{\circ}$ with the positive direction of

$x$ -axis.

Question 15

Find the equation of the straight line passing through

$(3,-2)$ and making an angle of

$60^{\circ}$ with the positive direction of

$y$ -axis.

Question 16

Find the equation of the straight lines which pass through the point

$(1,2)$ and are equally inclined to the axes.

Question 17

Find the equation of the straight line which passes through the point

$(1,2)$ and makes such an angle with the positive direction of

$x$ -axis whose sine is

$\frac{3}{5}$ ,

Question 18

Find the slope of the line passing through the points

$(3,4)$ and

$(1,2)$ . Also find its equation.

Question 19

Find the equation of the line passing through

$(-3,5)$ and perpendicular to the line through the points

$(2,5)$ and

$(-3,6)$ .

Question 20

(i) Find the equation of the right bisector of the line segment joining the points

$A(1,0)$ and

$B(2,3)$

(ii) Find the equation of the right bisector of the line segment joining the points

$(3,4)$ and

$(-1,2)$ .

Question 21

The perpendicular from the origin to a line meets it at the point

$(-2,9)$ , find the equation of the line.

Question 22

A line perpendicular to the segment joining the points

$(1,0)$ and

$(2,3)$ divides it in the ratio

$1: n$ . Find the equation of the line.

Question 23

Find the equation of the line through the point

$(0,2)$ making an angle

$\frac{\pi}{6}$ with the positive

$x$ -axis. Also find the equation of the line parallel to it and crossing the

$y$ -axis at a distance of 2 units below the origin.

Page no 21.32

Type 3

Question 24

Find the equation of the line passing through the points

$(2,3)$ and

$(5,-2)$

Question 25

Find the equation of the line passing through the following pair of points :

(i)

$(0,-3)$ and

$(5,0)$

(ii)

$(-1,1)$ and

$(2,-4)$

(iii)

$(1,-1)$ and

$(3,5)$

Question 26

Find the equation of the straight line which passes through the following two points :

(i)

$(a, b),(a+r \cos \alpha, b+r \sin \alpha)$

(ii)

$\left(a t_{1}^{2}, 2 a i_{1}\right),\left(a t_{2}^{2}, 2 a t_{2}\right)$

Question 27

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

$(2,1)$ ,

$(-2,3)$ and

$(4,5)$ .

Question 28

Using the concept of equation of a line, prove that the three point

$(3,0),(-2,-2)$ and

$(8,2)$ are collinear.

Question 29

The vertices of a triangle

$P Q R$ are

$P(2,1), Q(-2,3)$ and

$R(4,5)$ . Find the equation of the median through the vertex

$R$ .

Question 30

The Fahrenheit temperature

$F$ and absolute temperature

$K$ satisfy a linear equation. Given that

$K=273$ when

$F=32$ and

$K=373$ when

$F=212$ . Express

$K$ in terms of

$F$ and find the value of

$F$ when

$K=0$ .

KC Sinha Mathematics Solution Class 11 Chapter 21 Straight Lines Exercise 21.3

Exercise 21.3

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