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 \( y^{2}=4ax \) passing through \( D \) is \( (\alpha+\beta\sqrt{2},0) \), where \( \alpha \) and \( \beta \) are rational numbers, then \( \dfrac{\alpha}{\beta^{2}} \) is equal to:
