Let P(at2 ,2at) and \(Q\frac{a}{t^2},\frac{-2a}{t}\)
Equation of tangent at P ty = x+at2 .....(1)
Equation of tangent at Q \(-\frac{1}{t}y=x+\frac{a}{t^2}\)
y = –tx – a/t .....(2)
Point of intersection of both tangents, we get after sloving (1) & (2) i.e.
x+a = 0
A point lies on the directrix.