3. Given two distinct points $A$ and $B$, find the locus of points $M$ in the plane that satisfy the condition $\overrightarrow{M A} \cdot \overrightarrow{M B}=k^{2}$ (where $k$ is a non-zero real constant).
3. Let $|AB|=2a$, take the midpoint $O$ of $AB$, then $\overrightarrow{OA}=-\overrightarrow{OB} \cdot k^{2}=\overrightarrow{MA} \cdot \overrightarrow{MB}=(\overrightarrow{OA}-\overrightarrow{OM})$. $(\overrightarrow{OB}-\overrightarrow{OM})=(\overrightarrow{OA}-\overrightarrow{OM}) \cdot(-\overrightarrow{OA}-\overrightarrow{OM})=-\overrightarrow{OA}^{2}+\overrightarrow{OM}^{2}=|\overrightarrow{OM}|^{2}-a^{2}$, which means $|\overrightarrow{OM}|=$ $\sqrt{k^{2}+a^{2}}$. Therefore, the trajectory of point $M$ on the plane is a circle with the midpoint of $AB$ as the center and $\sqrt{k^{2}+a^{2}}$ as the radius.