Elliptic excenter loci for confocal or poristic ellipse pairs

Let a pair of ellipses admit Poncelet 3-periodics, and consider the loci of the excenters of the triangles in the family. The pair is poristic when the associated Poncelet family has the poristic property described in the source. Excenter-locus conjecture. The locus of the excenters is an ellipse if and only if the pair is either confocal or poristic. In the poristic case, the locus is a circle. The claim is supported by experimental evidence and by the cited known result that, in the poristic family, the excenter locus is a circle twice the radius of the circumcircle; the full if-and-only-if characterization remains open.

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Primary source

Mark Helman, Dominique Laurain, Dan Reznik and Ronaldo Garcia, “Poncelet Triangles: a Theory for Locus Ellipticity”, arXiv:2106.00715 (2021).

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