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

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?