The equation of the circle passing through intersection of circles, x2+y2+4x+6y−12=0 ....(I) And, x2+y2−6x−4y−12=0 .....(II) Is, x2+y2+4x+6y−12+λ(x2+y2−6x−4y−12)=0 Then, x2+y2+
4−6λ
1+λ
x+
6−4λ
1+λ
−12=0 ......(III) Since the another circle, x2+y2−4x+4y+8=0 ....(IV) Cut the circle (III) orthogonally then, −2(
4−6λ
1+λ
)+(
6−4λ
1+λ
)=8−12 −8+12λ+6−4λ=−4−4λ 12λ=−2 λ=−
1
6
So, required equation of circle is, 6(x2+y2+4x+6y−12)−(x2+y2−6x−4y−12)=0 5x2+5y2+30x+40y−60=0 x2+y2+6x+8y−12=0