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see the general equation in CL010 

H which is singular, X(1650) 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 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). 
