JEE Math Practice Question

For a > 0, let the curves C1 : y2 = ax and C2 : x2 = ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C1 and C2, and the area of $$\Delta $$OQR = $${1 \over 2}$$, then 'a' satisfies the equation :

1. A.x6 – 12x3 + 4 = 0
2. B.x6 – 12x3 – 4 = 0
3. C.x6 + 6x3 – 4 = 0
4. D.x6 – 6x3 + 4 = 0