Let the tangent drawn to the parabola y^2=24 x at the point (α, β) is perpendicular to the line 2 x+2 y=5. Then the normal to the hyperbola…

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