8. In the Cartesian coordinate system $x O y$, the focus of the parabola $y^{2}=2 x$ is $F$. Let $M$ be a moving point on the parabola. Then the maximum value of $\frac{M O}{M F}$ is $\qquad$ .
8. $\frac{2 \sqrt{3}}{3}$.

Let point $M(x, y)$. Then
$$
\begin{array}{l}
\left(\frac{M O}{M F}\right)^{2}=\frac{x^{2}+y^{2}}{\left(x+\frac{1}{2}\right)^{2}} \\
=\frac{4 x^{2}+8 x}{4 x^{2}+4 x+1} \\
=1+\frac{4 x-1}{4 x^{2}+4 x+1} .
\end{array}
$$
$$
\text { Let } 4 x-1=t \text {. }
$$

When $t \leqslant 0$, $\frac{M O}{M F} \leqslant 1$.
When $t>0$, we have
$$
\begin{array}{l}
\left(\frac{M O}{M F}\right)^{2}=1+\frac{4}{t+6+\frac{9}{t}} \\
\leqslant 1+\frac{1}{3}=\frac{4}{3},
\end{array}
$$

and when $t=3$, i.e., $x=1$, the equality holds.
Therefore, the maximum value of $\frac{M O}{M F}$ is $\frac{2 \sqrt{3}}{3}$.
At this time, point $M(1, \pm \sqrt{2})$.