The deal with an ellipse is that if you add the distances from any point on the curvy part to both of the foci, the sum is always the same. You can do this by using a thumb tack for each focus, and a string to make sure the distance is always the same. Planets, comets and asteroids all orbit the sun. They all follow a path that is shaped like an ellipse. If you draw the path of any orbit around the sun, you find that the sun is at one focus, and there isn't anything at the other focus.
Most comets have very eccentric orbits.
An epicycle is a small circle that some astronomers used to think a planet followed while it traveled in a much larger orbit. Ptolemy used epicycles to support his belief that the earth was the center of the universe, which is also not true. Copernicus used epicycles in a different way. He knew that each of the planets orbited the sun, but could not account exactly for the path that a planet followed. He assumed that planets traveled in a circular orbit .