I want to be able to determine where two ellipses intersect when they are over layed.

Each ellipse is the same size - same leght - same widths. The are over-layed such that their long axis bisect and are perpendicular.

For "minor" widths greater than zero, the ellipses would intersect at 4 points. If the points were connected, the would form a square.

If both ellipses were zero width they would look like a '+' sign and would all intersect at the origin (0).

I know the width and lenght and origin of the concentric ellipses.

How can I determine the intersect points? A radian lenght (distance from origin) would be okay - or a cartesian plot would also be good (either would derive the other, right?)