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 / c / Solution

The coordinate $x_1^{\prime }$ does not occur. The perpendicular cross-section isThus the surface is an elliptic cylinder extending in both directions along the zero-eigenvalue axis. Its cross-sectional semiaxes are $\sqrt{k/{\lambda }_2}$ and $\sqrt{k/{\lambda }_3}$. It becomes a circular cylinder when the two positive eigenvalues coincide.