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see the general equation in CL011 

X(99), X(805), X(877), X(880), X(892), X(5458) points at infinity of the sidelines of ABC 

K052 = A2(X115) is the locus of centers of conics circumscribed to the antimedial triangle having an asymptote passing through X(99). These conics are actually hyperbolas. K052 is a member of the class CL011 of cubics. K052 has three real asymptotes which are the parallels at E = X(4590) to the sidelines of ABC. The complement of K052 is K203. Its isogonal transform is K978 and its isotomic transform is K979. See here for a family of related cubics. *** A generalization by Angel Montesdeoca Let GaGbGc be the antimedial triangle and Q a fixed point. L(Q) is a variable line passing through Q. The locus of the center of the hyperbola circumscribed to GaGbGc and having L(Q) as an asymptote is the cubic cK(#Q, X2). This cubic is also the locus of the intersection S of L(Q) and the circumparabola whose axis is parallel to L(Q), S being the center of the hyperbola above. Examples : K015 = cK(#X2, X2) = nK(X2, X2, X2) K052 = cK(#X99, X2) = nK(X4590, X2, X99) K406 = cK(#X4, X2) = nK(X393, X2, X4) 
