The chord of contact of the tangents to the parabola x^2 = 4ay from an external point P(x,y) passes through point Q(0,2a). Find the equation of the locus of the midpoint of PQ

Points P(2p, p^2) and Q(2q, q^2) lie on the parabola x = 2t, y=t^2. Chord PQ passes through (0,2). If the tangent at P and the normal at Q intersect at point R, find the locus of R.

Find the locus of the midpoint M of all focal chords PQ where P(2ap, ap^2) and Q(2aq, aq^2) lie on the parabola x=2at, y=at^2

BIG thankyou to anyone who can help with these QS ! =D