Two equal circles with their centres on x and  y axis will possess the radical axis in the following form

Let (x−a)2+(y−0)2=r2 and x2+(y−b)2=r2 be two equal circles with their centres on x and y axes respectively.Then, their radical axis is given by −2ax+a2+2by−b2=0⇒2ax−2by+b2−a2=0Clearly, is of the form 2gx−2fy+g2−f2=0