If the two lines and cut the coordinate axes in concyclic points

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

If the two lines

a_1x + b_1y + c_1 = 0

and

a_2x + b_2y + c_2 = 0

cut the coordinate axes in concyclic points, prove that

a_1a_2 = b_1b_2

and find the equation of the circle.