The circle passing through the intersection of the circles, x 2 + y 2 - 6 x = 0 and x 2 + y 2 - 4 y = 0 having its centre on the line, 2 x - 3 y + 12 = 0 , also passes through the point :

Step-by-step solution

By family of circle, circle passing through intersection of given circles will be member of S 1 + λS 2 = 0  family  ( λ ≠ 1 ) x 2 + y 2 - 6 x + λ x 2 + y 2 - 4 y = 0 ( λ + 1 ) x 2 + ( λ + 1 ) y 2 - 6 x - 4 λy = 0 x 2 + y 2 - 6 λ + 1 x - 4 λ λ + 1 y = 0  Centre  3 λ + 1 , 2 λ λ + 1 Centre lies on 2 x - 3 y + 12 = 0 2 3 λ + 1 - 3 2 λ λ + 1 + 12 = 0 6 λ + 18 = 0 λ = - 3 Now circle is: x 2 + y 2 + 3 x - 6 y =