Parabola

A circle of radius 2 unit passes through the vertex and the focus of the parabola y² = 2x and touches the parabola \(y = {\left( {x - {1 \over 4}} \right)^2} + \alpha\), where \(\alpha\) > 0. Then (4\(\alpha\) \(-\) 8)² is equal to ______________.