Parabola

Let the tangent to the parabola \(\mathrm{y}^{2}=12 \mathrm{x}\) at the point \((3, \alpha)\) be perpendicular to the line \(2 x+2 y=3\). Then the square of distance of the point \((6,-4)\) from the normal to the hyperbola \(\alpha^{2} x^{2}-9 y^{2}=9 \alpha^{2}\) at its point \((\alpha-1, \alpha+2)\) is equal to _________.