The line y = mx + c intersects theparabola ${y}^{2}=4ax$ at the points P and Q.Show that the coordinates of the mid-point of PQ is $(\frac{2a-mc}{{m}^{2}},\frac{2a}{m})$.

If the mid-point is M, find the locus of M whenm varies and c = 1

If the mid-point is M, find the locus of M whenm varies and c = 1