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

Question

Philoid · Accepted Answer

Equation of a line whose intercepts on the axes are a and b is

⇒ bx + ay = ab

⇒ bx + ay – ab = 0 ………………..(1)

Perpendicular distance (d) of a line Ax + By + C = 0 from a point (x₁, y₁) is given by

Comparing equation (1) to the general equation of line i.e., Ax + By + C = 0, we obtain

A = b, B = a and C = -ab

If p is the length of the perpendicular from point (x₁, y₁) = (0, 0) to line (1), we obtain

⇒

Squaring both sides we get

⇒

∴