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see the general equation in CL011 

X(99), X(805), X(877), X(880), X(892), X(5458), X(17929), X(17930), X(17931), X(17932), X(17933), X(17934), X(17935), X(17936), X(17937) 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 the X(99)Hirst inverse of the Steiner circumellipse. 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) 
