The ordinates of the points $P$ and $Q$ on the parabola with focus $(3,0)$ and directrix $x=-3$ are in the ratio $3: 1$. If $R(\alpha, \beta)$ is the point of intersection of the tangents to the parabola at $P$ and $Q$, then $\frac{\beta^2}{\alpha}$ is equal to $\_\_\_\_$ :
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