Solve this following


For a > 0 , let the curves $C_{1}: y^{2}=a x$ and $C_{2}: x^{2}=$ ay intersect at origin $O$ and a point $P$. Let the line $\mathrm{x}=\mathrm{b}(0<\mathrm{b}<\mathrm{a})$ 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, $C_{1}$ and $C_{2}$, and the area of $\triangle \mathrm{OQR}=\frac{1}{2}$, then 'a' satisfies the equation

  1. $x^{6}-12 x^{3}+4=0$

  2. $x^{6}-12 x^{3}-4=0$

  3. $x^{6}+6 x^{3}-4=0$

  4. $x^{6}-6 x^{3}+4=0$

Correct Option: 1


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