Tangents at the extremities of a focal chord of aparabola intersect

Extremities of a focal chord are at2,2at,a/t2,−2a/tTangents are ty=x+at2, and −ty=xt2+aThey intersect at −a,at2−1t or −a,at−1twhich is the point of intersection of the directrixx = – a and the line y=at−1t which is theline through the mid-point of the chord parallel tothe axis.