The Lemoine ellipse is an inconic (that is always an ellipse) that has inconic parameters x:y:z = (2(b^2 + c^2) - a^2)/(b c) :(2(a^2 + c^2) - b^2)/(a c) : (2(a^2 + b^2) - c^2)/(a b). The triangle centroid G and the symmedian point K of the triangle are its foci, giving X_597 as its center.

Brianchon point | inconic | inellipse | Lemoine triangle