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