Coordinate Geometry: JEE Main 2022 Mathematics question

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 ______________.