If the length of the perpendicular from the point (1, 1) to the line ax – by + c = 0 be unity, Show that .

Question

Philoid · Accepted Answer

Given:

Line ax – by + c = 0 and point (1, 1)

To prove:

Concept Used:

Distance of a point from a line.

Explanation:

The distance of the point (1, 1) from the straight line ax − by + c = 0 is 1

∴ 1

⇒ a² + b² + c² – 2ab + 2ac – 2bc = a² + b²

⇒ ab + bc – ac

Dividing both the sides by abc, we get:

Hence proved.