Example 4 Find the range of $y=\sqrt{x^{2}-2 x+5}+$ $\sqrt{x^{2}-2 x+17}$.
Solution: The original expression can be rewritten as
$$
\begin{aligned}
y= & \sqrt{(x-1)^{2}+2^{2}}+ \\
& \sqrt{(x-1)^{2}+4^{2}},
\end{aligned}
$$

with a moving point $P(x, 0)$, and fixed points $A(1,2)$, $B(1,4)$. Clearly, $AB \parallel y$-axis, and the line segment $AB$ intersects the $x$-axis at $P(1,0)$, as shown in Figure 8.
When $x=1$, $y_{\text {min }}=|AB|=6$,
$\therefore$ the range is $[6,+\infty)$.