I'm not sure you can arbitrarily find the radii of an ellipse. Even worse, a free hand ellipse.

All the equations I know depend on r_{1}and r_{2}being know.

There may be a work around if you can calculate the area and/or circumference and then "reverse engineer" the equations, but don't know how reliable that will be.

If you find a way, be sure to post it and good luck.