Show that the locus of the midpoint M of the chord PQ is a parabola & Find the co-ordinates of its focus?

The points P(2ap,ap�) and Q(2aq,aq�), where p>q, lie on the parabola x� = 4ay, and the difference in their x-coordinates is 2a. Show that the locus of the midpoint M of the chord PQ is a parabola, and find the coordnates of its focus.