List of practice Questions

Reduce the following equations into slope-intercept form and find their slopes and the y-intercepts. 
(i) \(x + 7y = 0 \)
(ii) \(6x + 3y - 5 = 0 \)
(iii) \(y = 0\)
Reduce the following equations into intercept form and find their intercepts on the axes.
(i)  \(3x+2y-12=0\)
(ii)  \(4x-3y=6\)
(iii)  \(3y+2=0. \)
Find the distance of the point (–1, 1) from the line \(12(x + 6) = 5(y – 2)\)
Find the points on the x-axis, whose distances from the line \(\frac{ x}{3}+\frac{y}{4}=1\) are 4 units.
Find the distance between parallel lines
(i) \(15x + 8y – 34 = 0\) and \(15x + 8y + 31 = 0\)
(ii) \(l (x + y) + p = 0\) and \(l (x + y) – r = 0.\)
Find equation of the line parallel to the line \(3x - 4y + 2 = 0\) and passing through the point (-2, 3).
Find equation of the line perpendicular to the line \(x – 7y + 5 = 0\) and having x intercept 3.
Find angles between the lines \(\sqrt3x+y=1\) and \(x+\sqrt3y=1.\)
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.
Prove that the line through the point \((x_1, y_1)\) and parallel to the line \(Ax + By + C = 0 \) is \(A (x -x_1) + B (y - y_1) = 0.\)
Two lines passing through the point (2, 3) intersects each other at an angle of \(60º .\) If slope of one line is 2, find equation of the other line.
Find the equation of the right bisector of the line segment joining the points (3,4) and (–1,2).
Find the coordinates of the foot of perpendicular from the point \( (–1, 3) \) to the line \(3x – 4y – 16 = 0.\)
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.
If p and q are the lengths of perpendiculars from the origin to the lines  \(x \space cos θ − y \space sin θ = k\space  cos 2θ\) and \(x \space sec θ + y\space cosec θ = k\), respectively, prove that  \(p^2 + 4q^2 = k^2\)
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.
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  \(\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}.\)
Find the values of k for which the line (k – 3) x – (4 – k2) y + k2 – 7k + 6 = 0 is
(a) Parallel to the x-axis
(b) Parallel to the y-axis
(c) Passing through the origin