The straight line joining the points P(2p,p²) and Q(2q,q²) passes through the point (0,1)

a) i) Show that pq = -1

ii) Deduce the coordinates of R, the midpoint of PQ, are

(p - 1/p , 1/2(p² + 1/p²))

b) Find the cartesian equation of the locus of R as p varies, giving your answer in the form y=f(x)

OK i have attempted a lame start.

x=2p y=p²

p=x/2 y=(x/2)²

and now i'm stuck