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X(1), X(99), X(512), X(2142) = E(700), X(2143) = E(698), E(697), E(699)

excenters

Brocard points Ω1 and Ω2

This cubic is the isogonal circular pK with pivot X(512) with singular focus X(98).

Locus properties :

1. locus of point M such that the cevian triangles of M and its isogonal conjugate M* have the same area. See Cubics associated with triangles of equal area, Clark Kimberling, Forum Geometricorum, vol.1, 2001. This cubic is also called EAC1 = equal areas (first) cevian cubic.
2. Denote by Oa, Ob, Oc the circumcenters of triangles PBC, PCA, PAB respectively. The circumcenter of OaObOc lies on the perpendicular at O to the Brocard line if and only if P lies on the Brocard (fifth) cubic (together with C(O,R).