Example. Let $x^{2}+y^{2}-6 x-4 y+11=0$. Try to find the minimum and maximum values of $\mu=\sqrt{x^{2}+(y+1)^{2}}$.


Solve as shown in Figure 4, the equation $x^{2}+y^{2}-6x-6y+i1=0$ can be rewritten as $(x-3)^{2}+(y-2)^{2}=2$. It represents a circle with center C (3, 2) and radius $\sqrt{2}$. Thus, the problem is to find a point $(x, y)$ on $\mathrm{QC}$, such that the distance to the fixed point $\mathrm{A}(0,-1)$ is maximized or minimized. $\therefore|\mathrm{AC}|$
$$
\begin{array}{l}
=3 \sqrt{2}, \quad \therefore \mu_{\text{max}}=|A C|+\sqrt{2} \\
=4 \sqrt{2}, \quad \mu_{\text{min}}=|A C|-\sqrt{2}=2 \sqrt{2} .
\end{array}
$$