By the way, those green dots are called foci (the plural for focus -- it's one of those pretentious math words that make geeks feel superior.)

These points are pretty dang important!

In fact, our Sun lives at a focus... All the planets orbit the Sun in elliptical paths.

Notice how the Earth speeds up a bit when it gets closer to the Sun?

Coooooool! (Actually, it wouldn't be since you're closer to the Sun.)

(I exagerated this animation quite a bit too make my point. Although our orbits are ellipses, they are much closer to being circles.)

I know you're pretty dang jazzed about ellipses already (and, really, who can blame you), but, there's more!

These things have some totally amazing reflective properties!

Check it out:

If we shoot rays (like maybe light or sound) from one focus...

They shoot out, reflect off the inside of the ellipse and head straight for the other focus!

Repeat after me:  Duuuuuuuuuuuude!