y = –a is the correct solution. The other suggested solution does not work, because that equation is not satisfied by the coordinates of R.
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?