Let $\mathrm{A}(0,1), \mathrm{B}(1,1)$ and $\mathrm{C}(1,0)$ be the mid - points of the sides of a triangle with in Centre at the point D . If the focus of the parabola $y^2=4$ ax passing through $D$ is $(\alpha+\beta \sqrt{2}, 0)$, where $\alpha$ and $\beta$ are rational numbers, then $\frac{\alpha}{\beta^2}$ is equal to