The parametric equations of the parabola y2 = 8x are x = 2t2 and y = 4t. and the given equation of circle is x2+y2 – 2x – 4y = 0 On putting x = 2t2 and y = 4t in circle we get 4t4+16t2–4t2 – 16t = 0 ⇒ 4t2+12t2 – 16t = 0 ⇒ 4t (t3 + 3t – 4) = 0 ⇒ t(t – 1) (t2 + t + 4) = 0 ⇒ t = 0, t = 1 [Since t2 + t + 4 ≠ 0] Thus the coordinates of points of intersection of the circle and the parabola are Q (0, 0) and P(2, 4). Clearly these are diametrically opposite points on the circle. The coordinates of the focus S of the parabola are (2, 0) which lies on the circle ∴ Area of Δ PQS =