Circle

$x=0,\left(g^2+f^2\right) x-2 g f y=0$

$x=0,\left(g^2-f^2\right) x-2 g f y=0$

$y=0,\left(g^2-f^2\right) y-2 g f x=0$

$y=0,\left(g^2+f^2\right) y-2 g f x=0$