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