The Jerabek hyperbola is a circumconic that is the isogonal conjugate of the Euler line. Since it is a circumconic passing through the orthocenter, it is a rectangular hyperbola and has center on the nine-point circle. Its circumconic parameters are given by x:y:z = a[sin(2B) - sin(2C)]:b[sin(2C) - sin(2A)]:c[sin(2A) - sin(2B)], meaning it has trilinear equation (a[sin(2B) - sin(2C)])/α + (b[sin(2C) - sin(2A)])/β + (c[sin(2A) - sin(2B)])/γ = 0, or equivalently a(b^2 - c^2) S_A βγ + b(c^2 - a^2) S_B γα + c(a^2 - b^2) S_C αβ = 0 (P. Moses, pers. comm., Apr. 19, 2005), where S_A, S_B, and S_C are Conway triangle notation.
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