Integral Calculus: JEE Main 2026 Mathematics question

Let $P_1: y = 4x^2$ 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 bounded region enclosed between the line $y = \alpha x$, $\alpha > 0$ and $P_1$, then $\alpha$ is equal to :