Show that the normal line to a parabola at one of its points $P$ bisects the angle included between the focal radius of $P$ and the line through $P$ parallel to the axis of the parabola.
I'm trying to solving this by showing that $\tan α$ (the angle between the line from the focus through $P$ and the normal line) is equal to $\tan \beta$ (the angle between the normal line and the line parallel to the axis through point $P$). I've taken the parabola $4y=x^2$ so that the focus is $(0,1)$, the slope of the tangent line is $y'=m=\frac{x}{2}$ and the slope of the normal line is $m=-2x$. I'm using the following formula to derive $\tan \alpha$ and $\tan \beta$: $$\tan \phi=\frac{m_1-m_2}{1+m_1 m_2}$$ However, this formula isn't working for me when m is undefined (i.e., for the vertical line parallel to the axis).