A light ray is reflected in the interior of an ellipse, tracing out a region whose boundary is a hyperbola or a different ellipse within the original ellipse. Includes three questions, of increasing depth and complexity, to get students thinking about what's going on. For more on this type of thing, Google "dynamical billiards" or check out the excellent book "Mathematical Omnibus: Thirty Lectures on Classic Mathematics" by Fuchs and Tabachnikov.
