Poncelet triangles w/ circular caustic III: the loci of X2,X3,X4,X5

Let T=ABC be a family of Poncelet triangles interscribed between an outer ellipse E and an inner circular caustic K, centered at C. This video studies the foci of X(k), k=2,3,4,5, all on the Euler line, over C. Specifically, there are two positions of C on the major axis of E that cause X4 to shrink to a point which coincides with one of the foci of E.
Geogebra: www.geogebra.o...