I was inspired by the Feynman's Lost Lecture from 3blue1brown and minutephysics to recreate the ellipse diagram. Watch the video to understand what's going on here.
After I implemented this, I discovered there's also a Geogebra interactive version!
P.S. In the video, see the blob logo at 11:14!
Implementation note: lineWidth = 0.75, alpha = 1.0 produced a lot more icky moire effects than lineWidth = 1.5, alpha = 0.5. That's something I'll have to keep in mind for future projects.