Let the tangent drawn to the parabola \( y^2 = 24x \) at the point \( (\alpha, \beta) \) is perpendicular to the line \( 2x + 2y = 5 \). Then the normal to the hyperbola \( \dfrac{x^2}{\alpha^2} - \dfrac{y^2}{\beta^2} = 1 \) at the point \( (\alpha + 4, \beta + 4) \) does NOT pass through the point:
