Focal chords

The pole P of a focal chord H1H2 lies on the directrix. The connection of the pole P with the focus F1 is perpendicular to the chord:
The second focus F2 is reflected in the tangents at H1 and H2 to T1[F2] and T2[F2]. The two points are equally distant from P and equally distant from F1. Hence PF1 is perpendicular to T1T2

Kapitel und Portal
  Circle of reflexion Perpendicular chords