Past exam of the mathematical methods I course of the University of Oxford / 2022 / 8 / a / i

For $c>0$, this is the sphere centered at $\mathbf{a}$ with radius $c$. If $c=0$, its locus is the singleton $\{\mathbf{a}\}$; if $c<0$, it is empty, because a Euclidean norm cannot be negative. The equation describes the surface, not the enclosed ball.