You might find https://observablehq.com/@jrus/svg-elliptical-arcs useful

Ah! Definitely. I always appreciate your notebooks and hadn't seen this one. I understand the intuition behind that notebook, but the math is beyond me, so thank you for working through it!

It would definitely be clearer with several pictures. I originally intended to try to implement some interactive diagrams, but it has been 2.5 years so it would probably be better to start by just sketching a couple static diagrams with pen on paper.