TITLE: Rolling ellipses
QUESTION [10 upvotes]: I'm struggling to prove the following.
Set one ellipse in contact with a congruent one so that the minor axis of one is aligned with the major axis of the other. Now roll one round the other. The locus of the centre of the rolling ellipse is a circle centre the centre of the other, radius a + b.
Is there an obvious line of attack?

REPLY [8 votes]: As I promised, here is animation, that show locus point-by-point.

Ellipses parameters: $a=2, b=1$. 
Gray circle: circle with radius $3$.
Point of contact "moves" along static ellipse (and along rolling one) with constant speed.

Locus has some deviation of perfect circle.