A focal chord passes through the focus. If endpoints are at parameters t1 and t2, then t1*t2 = -1. If one end is ($at^2$, 2at), the other is (a/$t^2$, -2a/t). The length of a focal chord = a(t + 1/t)^2 = a(t - (-1/t))^2. The minimum focal chord length is 4a (the latus rectum), achieved when t = +/-1. Tangents at the endpoints of a focal chord are perpendicular and meet on the directrix.