## Inversive geometry question-ellipse and limacon

Hi,

I need to invert an ellipse about one of its foci. The ellipse in question has semi-minor axis of $\frac{\sqrt{2}}{2}$ and semi-major axis of 1.

After doing a little googling I see that the inverse of an ellipse about one of its foci is a "dimpled limacon." However, I am at a loss as to how to obtain the limacon equation for particular a and b values such as those indicated above.

Could someone please help?