Bounce balls inside an ellipse

I saw a post somewhere on this forum about objects bouncing inside an ellipse so I decided to continue my exploration of ellipses by having a go.

Assuming that the objects inside the ellipse travel in a straight line I extend my work on ellipse-ellipse intersections to include ellipse-line intersections.

The next stage was to calculate the ellipse perimeter normal vector at the point of intersection. At first I thought I would have to differentiate the implicit equation of a the ellipse, a task I wasn’t confident of being able to do. Fortunately there was a simple geometric paper and pen solution that was easy to code and with the perimeter normal I could easily calculate the rebound vector and this sketch was the result.