For a >0, let the curves C_1: y^2= a x and C_2: x^2= a y intersect at origin O and a point P. Let the line x= b (0< b < a ) intersect the chord OP…

For $\displaystyle \mathrm{a}>0$, let the curves $\displaystyle \mathrm{C}_1: y^2=\mathrm{a} x$ and $\displaystyle \mathrm{C}_2: x^2=\mathrm{a} y$ intersect at origin O and a point P. Let the line $\displaystyle x=\mathrm{b}(0<\mathrm{b}<\mathrm{a})$ intersect the chord OP and the $\displaystyle x$-axis at points Q and R, respectively. If the line $\displaystyle x=\mathrm{b}$ bisects the area bounded by the curves, $\displaystyle \mathrm{C}_1$ and $\displaystyle \mathrm{C}_2$, and the area of $\displaystyle \triangle \mathrm{OQR}=\frac{1}{2}$, then ' a ' satisfies the equation :