AP EAMCET Engineering 2018 Apr 23 Shift 2 Paper

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