Help with a non-canonical ellipse needed

I am accustomed to working with ellipses in canonical form. But I've got one that is definitely not in canonical form, and I am at a complete loss as to how to analyze it.

The original equations are these:

I need to figure out the long and short radiuses and the inclination angle of the long axis.

I am completely at an utter loss as to how to do this. I've tried to work with the equations every way I can think of, but I can't figure it out.

Any help would be welcome! :)