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see the general equation in CL010 

X(4), X(1650), X(57290), X(57291), X(57292), X(57293), X(57294), X(57295), X(57296) midpoints of ABC points at infinity of ABC sidelines vertices of the orthic triangle 

The Allardice cubic A1(H) is the locus of the center of a circumconic such that one of its asymptotes passes through H. The other asymptote envelopes the inconic with center O, perspector X(69). The tangents at the node H to A1(H) are those drawn from H to this inconic. K051 is a member of the class CL010 of cubics. K051 is the complement of cK(#X20, X2). 
