Consider the equation of circle, x2+y2+2gx+2fy+c=0........(i) When center is (−g,−f) then it must lie on the line, 2x+3y−7=0 2g+3f+7=0.................(ii) since equation (I) cuts the given circle so, x2+y2−4x−6y+11=0 x2+y2−10x−4y+21=0 Orthogonally, 2g(−2)+2f(−3)=c+11 4g+6f+c+11=0.......(iii) And, 2g(−5)+2f(2)=c+21 10g+4f+c+21=0.........(iv) From equation (III) and (IV), 6g−2f+10=0.........(v) From equation (II) and (V), 11f+11=0 f=−1 So, g=−2,c=3 Then 5g−10f+3c=5(−2)−10(−1)+33 =−10+10+9 =9