Two Ellipses In a Third

Two ellipses move within a third such that the two smaller ellipses are always tangent to each other and the larger one.

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X
0 0 6.283
a
0.5 0 2
b
0.25 0 1
h
-2 0 -0.5
k
1 0 4

All three ellipses are constrained only by their implicit equations. In the two smaller ellipses, this equation incluudes a function of X, the variable that controlls their rotation position within the larger ellipse. Can you figure out what the ellipses' equations are?

App generated by Geometry Expressions