Parabola

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 incentre at the point \(\mathrm{D}\). If the focus of the parabola \(y^{2}=4 \mathrm{ax}\) passing through \(\mathrm{D}\) is \((\alpha+\beta \sqrt{2}, 0)\), where \(\alpha\) and \(\beta\) are rational numbers, then \(\frac{\alpha}{\beta^{2}}\) is equal to :