Let P_1: y=4 x^2 and P_2: y=x^2+27 be two parabolas. If the area of the bounded region enclosed between P_1 and P_2 is six times the area of the…

Let $\displaystyle \mathrm{P}_1: y=4 x^2$ and $\displaystyle \mathrm{P}_2: y=x^2+27$ be two parabolas. If the area of the bounded region enclosed between $\displaystyle \mathrm{P}_1$ and $\displaystyle \mathrm{P}_2$ is six times the area of the bounded region enclosed between the line $\displaystyle y=\alpha x, \alpha>0$ and $\displaystyle \mathrm{P}_1$, then $\displaystyle \alpha$ is equal to :