An ellipse and a hyperbola share the same two foci. The semi-major axis of the ellipse is $a$, and the semi-transverse axis of the hyperbola is $e$. What are the lengths of the focal radii corresponding to the common points?
If the radii of the common points are $x$ and $y$, then

$$
x+y=2 a, \quad x-y=2 e
$$

from which

$$
x=a+e, \quad y=a-e
$$

Number of solutions: 16.