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.
(c) passing through the origin.
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 $K=0$.
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