Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / 6 / ii / a / Solution

Writing the common positive eigenvalue as $\lambda$, the equation is $|x^{\prime }{|}^2=k/\lambda$. Hence it is a sphere withEvery orthonormal set of axes is a principal-axis set in this fully degenerate case.