Find the locous of the intersection of tangents at R, given

P (2ap, ap^2) and Q (2aq, aq^2) are points on 4ay = x^2

Given that tangents are y = px - ap^2 and y = qx - aq^2

and PQ is a focal chord, passing through (0,a) meaning pq = -1

The point of intersection R is (a(p+q), apq)

is the locus y = -a ? or is it different, as in y = qx/ (1-q^2) as suggested by an answer?