Trace a moving midpoint locus from tangent intercepts

For $x=t^2$, $y=2/t$:

(i) Find and simplify the tangent equation at $(p^2,2/p)$.

(ii) Hence find Q and R where that tangent meets the x- and y-axes, respectively.

(iii) Find a Cartesian equation for the locus of the midpoint of QR as p varies.