Optical Properties of Elliptical Mirrors
Elliptical mirror showing that rays passing through one focus also pass through the other - Math Open Reference

An ellipse has two focus points (foci) which always lie on the major (longest) axis, spaced equally each side of the center.

If the inside of an ellipse is a mirror, any light ray leaving one focus will always pass through the other. In the figure above, every light ray leaving F1 reflects off the inside of the elliptical mirror and bounces back, passing through the other focus F2.

When a light ray bounces off the elliptical mirror, it acts as though it had been reflected off a flat mirror which is tangential to the ellipse at that point. See Tangent to an Ellipse.

It works for sound too

Similarly, sound waves leaving one focus will pass through the other focus. If one person stands in an elliptical room on one focus, another person standing at the other focus will hear the other's voice as if he were standing right next to him.

Other ellipse topics