Prove that the product of the lengths of the perpendiculars drawn from the points and to the line

The equation of the given line is

⇒ bxcosƟ + aysinƟ – ab = 0 ……………….(1)

Length of the perpendicular from point to line (1) is

--------------- (2)

Length of the perpendicular from point to line (2) is

--------------- (3)

On multiplying equations (2) and (3), we get,

Hence Proved.