For what relation will the circle touch each other $S_1=x^2+y^2+2gx+2fy=0$ and $S_2=x^2+y^2+2g'x+2f'y=0$?

Question

$\begin{array}{1 1}(a)\;gf'=g'f\\(b)\;gf'=-g'f\\(c)\;g'f'=g'f\\(d)\;gf'=g'ff'\end{array}$