# More reflections in an ellipse?

This is a follow-up to a question that was answered quite well a few days ago:

http://answers.yahoo.com/question/index;_ylt=Atjux...

From a point on an ellipse, a point particle is projected across the interior, tracing a chord. At the point where it intersects the ellipse it rebounds back across the interior again, subject to the reflective properties of an ellipse. It then traces another chord and rebounds again. This continues indefinitely. The first chord does not go through either focus.

The path may or may not retrace the first chord. Suppose that it does not. Describe the pattern traced by the path.

### 1 Answer

- 10 years agoFavourite answer
I'm still wondering how to prove analytically the case when an ellipse or hyperbola is formed.

Here's a link for a geometric proof (see page183, 184):

http://books.google.com/books?vid=ISBN0521587506&i...

Article that seems to suggest an analytical proof is possible: