The equation of a circle passing through the points of intersection of the circles x 2 + y 2 - 4 x - 6 y - 12 = 0 , x 2 + y 2 + 6 x + 4 y - 12 = 0 and having radius 13 is

Step-by-step solution

The equation of a circle passing through the points of intersection of the circles, x 2 + y 2 - 4 x - 6 x - 12 + λ x 2 + y 2 + 6 x + 4 y - 12 = 0 x 2 ( 1 + λ ) + y 2 ( 1 + λ ) + x ( 6 λ - 4 ) + y ( 4 λ - 6 ) - 12 λ - 12 = 0 Rewrite the above equation.  x 2 + y 2 + x ( 6 λ - 4 ) ( 1 + λ ) + y ( 4 λ - 6 ) ( 1 + λ ) - 12 = 0 On comparing in equations with  x 2 + y 2 + 2 g x + 2 f y + c = 0 g = ( 3 λ - 2 ) ( 1 + λ ) , f = ( 2 λ - 3 ) ( 1 + &#955