The given parabola is y2 = 4x .....(1)
This line cuts the x-axis (the axis of the parabola) at (4, 0) which is a fixed point for all positions of P.
Let R(α,β) be the middle point of PQ. Then α = t12 + t22 .....(3)
and β = t1 + t2
From (4),β2 = t1 2 + t2 2 + 2t1 t2 = 2α – 8 [From (2) and (3)] Hence Locus of R (α, β) is y2 = 2x – 8