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too complicated to be written here. Click on the link to download a text file. 

infinite points of the sidelines of ABC 

Q077 is the locus of foci of circumparabolas. 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 circumparabola 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 circumparabola. The isogonal conjugate of Q with respect to the anticevian triangle of P is a point F on Q077. 
