Question

From the origin, chords are drawn to the circle (x – 1)² + y² = 1. Find the equation to the locus of the middle points of these chords. 

Answer 1

Let (h, k) be middle points 

Equation of chord through (h, k) is

As the chord given by equation (i) passes through (0, 0) 

∴ On substituting, x = 0 and y = 0, we get