I'm having problems with a few parametric equation questions. Considering how much trouble I've been having with this particular unit of work, I expect I'll have to use this thread to ask more questions in the near future. The one I'm stuck on at the moment is;

PQ, a variable chord of the parabola , subtends a right angle at the vertex O.

a) If p and q are parameters corresponding to P and Q, show that pq = -4.

b) If the tangents at P and Q intersect at T, find the locus of T.

c) If M is the midpoint of chord PQ, determine the locus of M.