A circle of radius 2 unit passes through the vertex and the focus of the parabola y^2=2 x and touches the parabola y=(x-1/4)^2+α, where α>0. Then (4…

A circle of radius $\displaystyle 2$ unit passes through the vertex and the focus of the parabola $\displaystyle y^2=2 x$ and touches the parabola $\displaystyle y=\left(x-\frac{1}{4}\right)^2+\alpha$, where $\displaystyle \alpha>0$. Then $\displaystyle (4 \alpha-8)^2$ is equal to \_\_\_\_.