Parabola tangent normal hyperbola

Let the tangent to the parabola y2=12x at the point (3,α) be perpendicular to the line 2x+2y=3. Then the square of distance of the point (6,−4) from the normal to the hyperbola α2x2−9y2=9α2 at its point (α−1,α+ 2 ) is equal to _______.