> Not surprisingly, the other intersections of the ellipse with the sidelines of ABC (besides the midpoints) are the points where the angle bisectors (i.e cevians of X(1)) intersect the sidelines.
> This can be generalized as: The locus of the centers of all conics passing through four points A,B,C,D is another conic centered at the centroid of ABCD and passing through the pairwise midpoints of A,B,C and D and the intersections of the 3 diagonals of ABCD.
The new Conic you found is the Nine-point conic.
Again a very interesting conic indeed!
Chris van Tienhoven