Equation of locus of two tangents

If the normal at to the parabola meets the curve again at prove that . Prove that the equation of the locus of the point of intersection of he tangents to the parabola at P and Q is

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I've done the first part of proving .

for this second part, I tried to find a parametric equation for the locus the point of intersection of the tangents. Found the equation of the two tangents, then the point of intersection. The problem I have is there is no p or q in the equation I'm supposed to prove, while the point is in terms of p and q. Need someone to point me in the right direction and I should be able to finish off. Thanks!