Consider the circle C: x^2+y^2=4 and the parabola P: y^2=8 x. If the set of all values of α, for which three chords of the circle C on three distinct…

Consider the circle $\displaystyle C: x^2+y^2=4$ and the parabola $\displaystyle P: y^2=8 x$. If the set of all values of $\displaystyle \alpha$, for which three chords of the circle $\displaystyle C$ on three distinct lines passing through the point $\displaystyle (\alpha, 0)$ are bisected by the parabola $\displaystyle P$ is the interval $\displaystyle (p, q)$, then $\displaystyle (2 q-p)^2$ is equal to $\displaystyle \_\_\_\_$.