See discussion at http://scratch.mit.edu/discuss/topic/94194/ Manually fit an ellipse specified by axes and a shear to the same shape specified in a more traditional style by axes and rotation. Can you determine a mathematical mapping of one style of specification to the other? I maintain that it is always possible to map one to the other. Somehow. There are almost certainly multiple mappings. You are unlikely to need to change the positional x,y parameters. If you tweak scale, you can normalise when you're done by multiplying the axes by that value before setting it to 1.
It does everything for you now!