If the two circles x2+y2+2gx+2fy=0 and x2+y2+2g1x+2f1y=0 touch each other then
ff1=gg1
(fg_1 = f_1g\)
f2+g2=f21+f21
fg1=f1g1
|r1±r2|=C1C2|√g2+f2±√g21+f21|=√(g−g1)2+(f−f1)2⇒gf1=fg1
If the two circles x2+y3+2gx+2fy=0 and x2+y2+2g1x+2f1y=0 touch each other then