$\text{ For a }>0,\text{ let the curves }{\mathrm{C}}_1:{\mathrm{y}}^2=\mathrm{ax}\text{ and }{\mathrm{C}}_2:{\mathrm{x}}^2=\text{ ay intersect at origin }\mathrm{O}\text{ and a point }\mathrm{P}\text{ . }$

$\text{ Let the line }\mathrm{x}=\mathrm{b}(0<\mathrm{b}<\mathrm{a})\text{ intersect the chord }\mathrm{OP}\text{ and the }\mathrm{x}\text{ -axis at points }\mathrm{Q}\text{ and }\mathrm{R}\text{ , }$

$\text{ respectively. If the line }\mathrm{x}=\mathrm{b}\text{ bisects the area bounded by the curves, }{\mathrm{C}}_2\text{ and }\mathrm{C},\text{ and the area }$

$\text{ of }\Delta \mathrm{OQR}=\frac{1}{2},\text{ then 'a' satisfies the equation: }$

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