CBSE - Class 11 Mathematics Straight Lines Worksheet
EXERCISE 9.3
1.
Find angles between the lines $\sqrt{3}x + y = 1$ and $x + \sqrt{3}y = 1$.
2.
Reduce the following equations into intercept form and find their intercepts on the axes. (iii) $3y + 2 = 0$.
3.
Find the distance of the point (–1, 1) from the line $12(x + 6) = 5(y – 2)$.
4.
Find equation of the line perpendicular to the line $x – 7y + 5 = 0$ and having x intercept 3.
5.
If $p$ and $q$ are the lengths of perpendiculars from the origin to the lines $x \cos\theta - y \sin\theta = k \cos 2\theta$ and $x \sec\theta + y \csc\theta = k$, respectively, prove that $p^2 + 4q^2 = k^2$.
6.
Reduce the following equations into intercept form and find their intercepts on the axes. (ii) $4x – 3y = 6$
7.
The perpendicular from the origin to the line $y = mx + c$ meets it at the point (–1, 2). Find the values of $m$ and $c$.
8.
Find equation of the line parallel to the line $3x - 4y + 2 = 0$ and passing through the point (–2, 3).
9.
Two lines passing through the point (2, 3) intersects each other at an angle of $60^\circ$. If slope of one line is 2, find equation of the other line.
10.
Find the distance between parallel lines (i) $15x + 8y – 34 = 0$ and $15x + 8y + 31 = 0$
11.
Find the distance between parallel lines (ii) $l (x + y) + p = 0$ and $l (x + y) – r = 0$.
12.
Prove that the line through the point ($x_1$, $y_1$) and parallel to the line $Ax + By + C = 0$ is $A (x –x_1) + B (y – y_1) = 0$.
13.
The line through the points ($h$, 3) and (4, 1) intersects the line $7x - 9y - 19 = 0$ at right angle. Find the value of $h$.
14.
If $p$ is the length of perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$, then show that $\frac{1}{p^2} = \frac{1}{a^2} + \frac{1}{b^2}$.
15.
Reduce the following equations into intercept form and find their intercepts on the axes. (i) $3x + 2y – 12 = 0$
16.
Reduce the following equations into slope - intercept form and find their slopes and the y - intercepts. (iii) $y = 0$.
17.
In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.
18.
Reduce the following equations into slope - intercept form and find their slopes and the y - intercepts. (ii) $6x + 3y – 5 = 0$
19.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).
20.
Reduce the following equations into slope - intercept form and find their slopes and the y - intercepts. (i) $x + 7y = 0$
