# Simplify rational expression to polynomial

I'd like to check my computations for rational polynomial equations with sage. Here is an equation that gives the general form of a parabola with respect to a directrix and focus:

(ax+by+c)^2/(a^2+b^2) = (x-f1)^2 + (y-f2)^2

I'd like to obtain from this rational expression a polynomial expression in x,y. Is there a way to do this kind of computation automatically in Sage?

Take the numerator of the difference.