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infinite points of the sidelines of ABC

Q077 is the locus of foci of circum-parabolas.

Q077 is a circular quintic with three real asymptotes forming a triangle homothetic of ABC under the homothety h(G, 1/4) and two other imaginary asymptotes concurring at X(143), the nine point center of the orthic triangle.

It follows that the three circles with centers A, B, C passing through any point F on Q077 must have a common tangent, the directrix of the circum-parabola with focus F.

Construction of Q077 :

Let L be a variable line passing through G (or any other point). The complement of the isotomic conjugate of the infinite point Q of L is the perspector P of a circum-parabola. The isogonal conjugate of Q with respect to the anticevian triangle of P is a point F on Q077.