A focal chord has endpoint parameters satisfying t1t2=-1. If one end is t, the other is -1/t. Length = a(t+1/t)^2, minimized at t=+/-1 giving 4a (the latus rectum). Sum of focal distances of endpoints = a($t^{2+1}$/$t^{2+2}$). The harmonic mean of the two focal distances equals the semi-latus rectum 2a. Tangents at focal chord endpoints are perpendicular and meet on the directrix. The circle with a focal chord as diameter touches the directrix. The locus of the midpoint of focal chords is the parabola $y^2$=2a(x-a). For the focal chord making angle theta with the axis, its length is 4a/$sin^2$(theta), which is 4a*$cosec^2$(theta).