13. Let $P$ be a moving point on the circle $x^{2}+y^{2}=36$, and point $A(20,0)$. When $P$ moves on the circle, the equation of the trajectory of the midpoint $M$ of line segment $P A$ is $\qquad$.
13. $(x-10)^{2}+y^{2}=9$.

Let $M(x, y) 、 P\left(x_{0}, y_{0}\right)$. Then
$$
\begin{array}{l}
x=\frac{x_{0}+20}{2}, y=\frac{y_{0}}{2} \\
\Rightarrow x_{0}=2 x-20, y_{0}=2 y .
\end{array}
$$

Since point $P$ is on the circle, we have
$$
(2 x-20)^{2}+(2 y)^{2}=36 \text {. }
$$

Therefore, the trajectory of point $M$ is $(x-10)^{2}+y^{2}=9$.