I thought I'd just post a sampler of what is happening on my other digital stomping grounds. This starts with two circles that can rotate around two circles with the same center. They are rotating in different directions, but their orbits take the same amount of time. The end creation is an ellipse. Below is a derivation of a Cartesian equation as an #Algebra II or #PreCalc student might do it.
The important thing here is that dynamic geometry such as #GeoGebra can open doors to concepts not normally seen until later years. The basic construction here (minus the buttons and check boxes) can be handled by a middle school student. The entire GeoGebra file can be found here.