x2+y2+2gx+2fy+c=0 cuts orthogonally the circle x2+y2−4x−6y+11=0 and x2+y2−10x−4y+21=0 ∴−4g−6f=c+11 . . . (i) and −10g−4f=c+21 . . . (ii) Centre of circle x2+y2+2gx+2fy+c=0 is lie in bisector of angle betweenthe positive coordinate axis ∴g=f . . . (iii) ⋅s From Eqs. (i) and (iii), we get −4f−6f=c+11 −10f=c+11 . . . (iv) From Eqs. (ii) and (iii), we get −14f=c+21 . . . (v) From Eqs. (iv) and (v), we get g=f=