Three. (Full marks 23 points) Given that $M$ is a point on the moving chord $AB$ of the parabola $y^{2}=$ $2 p x$, $O$ is the origin, $O A$ $\perp O B, O M \perp A B$. Find the equation of the locus of point $M$.


Three, let $A B$ intersect the $x$-axis at point $C\left(x_{0}, 0\right)$, and the coordinates of $A, B$ are $\left(x_{1}, y_{1}\right)$, $\left(x_{2}, y_{2}\right)$, respectively. Then
$$
\begin{array}{l}
y_{1}^{2}=2 p x_{1}, \\
y_{2}^{2}=2 p x_{2} . \\
\because O A \perp O E, \\
\therefore \frac{y_{1} y_{2}}{x_{1} x_{2}}=-1,
\end{array}
$$

which means
$$
y_{1} y_{2}=-4 p^{2} \text {. }
$$

The equation of the line $A B$ is
$$
\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}},
$$

Substituting point $C$ into it, we get
$$
\frac{-y_{1}}{x_{0}-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} .
$$

Simplifying, we obtain $x_{0}=2 p$. Therefore, the equation of the locus of $M$ is
$$
(x-p)^{2}+y^{2}=p^{2} .(x \neq 0)
$$