8 Given that $A B C D E F$ is a regular hexagon with side length 2, a parabola passes through points $A$, $B$, $C$, and $D$. Then, the distance from the focus to the directrix of the parabola is $\qquad$
$8 \frac{\sqrt{3}}{2}$ Hint: Establish a Cartesian coordinate system such that the coordinates of $A, B, C, D$ are $(-2, \sqrt{3}), (-1,0), (1,0), (2, \sqrt{3})$, respectively. Then, the equation of the parabola can be found to be $\sqrt{3} y=x^{2}-1$. Therefore, the distance from the focus to the directrix of the parabola is $\frac{\sqrt{3}}{2}$.