We have, S≡x2+y2+2gx+2fy+6=0 cuts another circle x2+y2−6x−6y−6=0 orthogonally. ‌⇒2g1g2+2f1f2=c1+c2 ‌2g(−3)+2f(−3)=6−6⇒g+f=0 and angle between S=0 and x2+y2+6x+6y+2=0‌ is ‌60∘. The condition for angle θ between two circles is given by cos‌θ‌=‌
