IMO 1983 LL VIE74
In a plane we are given two distinct points A, B and two lines
IMO 1983 LL VIE74
Origin: VIE
Problem
In a plane we are given two distinct points A, B and two lines a, b passing through B and A respectively (a ∋B, b ∋A) such that the line AB is equally inclined to a and b. Find the locus of points M in the plane such that the product of distances from M to A and a equals the product of distances from M to B and b (i.e., MA \cdot MA′ = MB \cdot MB′, where A′ and B′ are the feet of the perpendiculars from M to a and b respectively).