Find the locus equation of points that are equidistant from the fixed line $1: x=-\frac{p}{2}$ and the fixed point $F\left(\frac{p}{2}, 0\right)$.
Let $M (x, y)$ be any point on the trajectory, then it must lie on the line at a distance of $\mathrm{d}$ from 1 and on the circle centered at $\mathrm{F}$ with radius $\mathrm{d}$. Therefore,
$$
\left\{\begin{array}{l}
x=d-\frac{p}{2} \\
\left(x-\frac{p}{2}\right)^{2}+y^{2}=d^{2}
\end{array}\right.
$$

Eliminating the parameter $d$;
$$
x^{2}-p x+\frac{p^{2}}{4}+y^{2}=x^{2}+p x+\frac{p^{2}}{4},
$$

we obtain the parabola equation
$$
y^{2}=2 p x
$$