X(2), X(76), X(141), X(257), X(297), X(335), X(384), X(385), X(694), X(698), X(1916), X(2998)
X = X(14970) = isotomic conjugate of X(732)
infinite points of the Steiner ellipse
Let A1B1C1 be the first Brocard triangle and M a variable point. The lines MA1, MB1, MC1 meet BC, CA, AB at Ma, Mb, Mc respectively. These three points are collinear if and only if M lies on K017. They form a triangle perspective to ABC if and only if M lies on K020. In this case, the locus of the perspector is K322.
K322 meets the line at infinity at X(698) and the infinite points of the Steiner ellipse hence K322 has only one real asymptote. The "last" common point with the Steiner ellipse is the isotomic conjugate of X(732).
See a generalization at CL041.