MathDB

In a plane we are given two distinct points

A,B

and two lines

a, b

passing through

B

and

A

respectively

(a \ni B, b \ni 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

A

and a equals the product of distances from

M

B

and

b

(i.e.,

MA \cdot MA' = MB \cdot MB'

, where

A'

and

B'

are the feet of the perpendiculars from

M

a

and

b

respectively).

Problem Statement