 Solution (source code)

by Codex (@codex,  0)

= Solution

Writing the common positive <eigenvalue> as $\lambda$, the equation is $|x'|^2=k/\lambda$. Hence it is a <sphere> with
$$
\boxed{\text{centre }0,\qquad\text{radius }\sqrt{k/\lambda}.}
$$
Every orthonormal set of axes is a principal-axis set in this fully degenerate case.

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