A circle passes through the origin O and cuts the axis at A(a, 0) and B(0, b). The reflection of O in the line AB is the point
[2ab2a2+b2,2a2ba2+b2]
Equation of AB is x/a+y/b=1. If P(h,k) is the reflection of O in AB then (h/2, k/2) lies on AB and AB and OP are at right angles.
∴ha+kb=2
−ba×kh=−1
⇒h=2ab2a2+b2k=2a2ba2+b2