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The Locus of the centers of all Conics through the Vertices and Orthocenter of a Triangle (which are Rectangular Hyperbolas when not degenerate), is a Circle through the Midpoints of the sides, the points half way from the Orthocenter to the Vertices, and the feet of the Altitude.
See also Altitude, Conic Section, Feuerbach's Theorem, Kiepert's Hyperbola, Midpoint, Orthocenter, Rectangular Hyperbola
References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 198, 1959.