Parabola

The parabola is x = 2t2, y = 4t.
Solving it with the circle, we get
4t4+16t2−4t2−16t=0
⇒ t4+3t2−4t = 0 ⇒ t = 0 , 1
Hence, the points P and Q are (0, 0) and (2, 4), respectively, which are also diametrically opposite points on the circle. The focus is S ≡ (2,0).
The area of ΔPQS =

1

2

×2×4 = 4.