Let ABC be a triangle and L a line passing through X(850). Let P1, P2 denote the brocardians of a point P on L, and P1', P2' its isotomic conjugates. The envelope of line P1'P2' is a parabola as P moves on L. The locus of its focus is the Parry circle as L moves around X(850). As L moves around X(850) the directrix of the parabola passes through X(5996), on the line through centroid parallel to line of the 1st and 2nd Brocard points.
A more general approach in: http://amontes.webs.ull.es/otrashtm/HGT2016.htm#HG161116
Angel Montesdeoca
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