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X(1), X(36), X(40), X(80), X(84), X(102), X(515)

Ia, Ib, Ic : vertices of the excentral triangle

Ja, Jb, Jc : their reflections in the sidelines of ABC

cevian points of X(515)

K269 is the locus of point M such that the reflections of M in the sidelines of ABC form a triangle perspective with the excentral triangle IaIbIc. The locus of the perspector is another (not very exciting) cubic.

K269 is an isogonal circular pK with pivot X(515), the infinite point of IH, with asymptote the parallel at X(102) to IH, with singular focus X(109).

K269 belongs to the class CL035 of cubics. See also Table 6.