Mathematics - Parabola Question with Solution | TestHub

For$a>0,$let the curves$C_1:y^2=ax$and$C_2:x^2=ay$intersect at origin$O$and a point$P.$Let the line$x=b\left(0<b<a\right)$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$∆OQR=\frac{1}{2},$then ‘$a$’ satisfies the equation: