I wanted to test the statement in this video that only a parabola is capable of focusing to a single point. The interactive graphic on eccentricity on this site gave me an idea of how to approach this.

A couple of Desmos programs later, and with a better appreciation for why Newton invented calculus, here is the end result!

This is probably a round about way to go about it. But hey, it’s also a good excuse to do some maths!

Move mouse across to interact.