linguistic:paraphrasing, structural:reformatting, structural:summarization
Intersection of a sphere with a more general surface

If a sphere is intersected by another surface, there may be more complicated spherical curves.

The intersection of the sphere with equation x 2 + y 2 + z 2 = r 2 {\displaystyle \;x^{2}+y^{2}+z^{2}=r^{2}\;} and the cylinder with equation (y − y 0) 2 + z 2 = a 2, y 0 ≠ 0 {\displaystyle \;(y-y_{0})^{2}+z^{2}=a^{2},\;y_{0}\neq 0\;} is not just one or two circles. It is the solution of the non-linear system of equations

(see implicit curve and the diagram)