Is it possible that we rotate a circle around an ellipse when the distance from the center of the circle to the ellipse is always the same?
I have tried consider the center of the circle $(x_0,y_0)$ as: $$x_0=(a+R)\cos t,\\ y_0=(b+R) \sin t$$ where $a$ and $b$ are the major and minor semi-axis of the ellipse, respectively, and $R$ is the radius of the circle, for $t\in[0,2\pi)$. Then the center of the circle move on another ellipse with two semi-axis: $(a+R)$ and $(b+R)$
I found out that this is wrong. I was wondering if it is possible to do that.