TS EAMCET 03 May 2019 Shift 2 Solved Paper

The equation of given circles are
x2+y2−4x−6y+4=0
x2+y2+6x−4y+15=0
Let the circle be x2+y2+2gx+2fy+c=0 that cuts the above two circles orthogonally.
−4g−6f‌‌=c+4
6g−4f‌‌=c+15
Solve the equations
3g=4
Circle also passes through (1,1)
1+1+2g+2f=0
2g+2f+c=−2
Now
5g+2f+c=3g+(2g+2f+c)
=4−2=2