The question was:
The points P and Q on the curve: $$x = 2at, y= at^2$$ have parameters p and q respectively. Show that PQ intersects the directrix at: $$ \left (\frac{2a(pq-1)}{p+q},-a \right ) $$
I've managed to find that the equation of the chord PQ is: $$ y - \frac{1}{2} (p+q)x+apq=0 $$ but after this I'm a bit confused has to how to find the directrix using a parametric equation.