Let A (0,1), B (1,1) and C (1,0) be the mid-points of the sides of a triangle with incentre at the point D. If the focus of the parabola y^2=4 ax…

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