17. Given a moving circle that is externally tangent to the fixed circle $|z-(1+\mathrm{i})|=2$, and internally tangent to the fixed circle $|z-(1-5 \mathrm{i})|=10$, find the locus of the center of the moving circle.
17. The equation of the locus of the center of the required moving circle is $|z-(1+i)|+|z-(1-5 i)|=12$, which represents an ellipse with foci at $(1,1)$ and $(1,-5)$, and a major axis length of 12.