Straight Lines ...

A line cutting off intercept – 3 from the y-axis and the tangent at angle to the x axis is \(\frac{3}{5},\) its equation is

Slope of a line which cuts off intercepts of equal lengths on the axes is

The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is

The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is

If the line \(\frac{x}{a} + \frac{y}{b} = 1\) passes through the points (2, –3) and (4, –5), then (a, b) is

The distance of the point of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is

The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line \(\sqrt 3 x + y = 1\) is

The equations of the lines passing through the point (1, 0) and at a distance \(\frac{\sqrt3}{2}\) from the origin, are

The distance between the lines y = mx + \(c_1\) and y = mx + \(c_2\) is

The coordinates of the foot of perpendiculars from the point (2, 3) on the line y = 3x + 4 is given by

Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is

For specifying a straight line, how many geometrical parameters should be known?

The point (4, 1) undergoes the following two successive transformations :

(i) Reflection about the line y = x

(ii) Translation through a distance 2 units along the positive x-axis

Then the final coordinates of the point are

A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y- intercept is