The long and short radii a and b of an ellipse lie on the hyperbola a2 – b2 = f2, where f is half the distance between the foci.
Your mouse points to one of the foci, and the left and right arrow keys change the ratio
You may need to click the display before it will pay attention to your keyboard input.
Here's the source code.
Written in Processing, and licensed under a Creative Commons Attribution 4.0 International License.