Find equation of curve equidistant from two ellipses

Question

For visualizing some geometric curve, I have to choose a way between finding sampling points on the curve by numerical processing and finding curve equation of that curve.

The curve that I want to visualize is equidistant from two different ellipses.

Each length of major axis, minor axis, and the angle between x-axis and major axis of two ellipse is given.

I think there can be two inflection points on the curve. What is the equation of that curve?

The blue curve on upper image is the result from numerical processing.

Answer 1

This is in general a difficult calculation.

Farouki, Rida T., and John K. Johnstone. "Computing point/curve and curve/curve bisectors." IMA Conference on the Mathematics of Surfaces. 1992. (PDF download.)

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Ramamurthy, Rajesh, and Rida T. Farouki. "Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I. Theoretical foundations." Journal of Computational and Applied Mathematics 102.1 (1999): 119-141.

See also this Inst. Math & Appl website, Voronoi Diagram of Ellipses:

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