Director Circle of a Conic Inscribed in a Triangle

Extract

Let TP, TQ (Fig. i.) be tangents to a conic, C its centre, S, H its foci, 2a and 2b its axes. From S draw a perpendicular to TP and produce it to its image S′; then we know that S′T = ST, angle S′TP = PTS, and S′H = major-axis = 2a. Similarly with a perpendicular drawn from H to TQ and produced to its image H′. Thus the two triangles S′TH and STH′ are equal, and the angles S′TS, HTH′, and therefore the halves of these angles, are equal, that is, “the tangents from T are equally inclined to the focal distances of T.′