Alberto Mendoza, Three conics derived from perpendicular lines,
Forum Geometricorum, 12 (2012) 131--139.

Abstract.   Given a triangle ABC and a generic point P on its plain, we consider the rectangular hyperbola H which is the isogonal conjugate of the line OP where O is the circumcenter of the triangle. We also consider the line L perpendicular to OP at the point P, the conic E which is the isogonal conjugate of this line and the inscribed parabola, tangent to the line L. We discuss some relations between this three conics.

[ps file] [pdf]