Re: [math-fun] Poncelet's porism overpush?

Every pair of cleanly nested ellipses can be converted to a pair of circles under a suitable projective transformation. Specifically, we take a (complex conjugate!) pair of intersection points, and map them to the two circular points at infinity using a projective transformation with real coefficients: https://en.wikipedia.org/wiki/Circular_points_at_infinity So both of the questions:

*Arbitrary* (cleanly nested) ellipses? Don't they both need to be circles under the same projection?

are true, because they're equivalent. Best wishes, Adam P. Goucher