Hyperbola

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