Solution
= Solution
The coordinate $x_1'$ does not occur. The perpendicular cross-section is
$$
\frac{x_2'^2}{k/\lambda_2}+\frac{x_3'^2}{k/\lambda_3}=1.
$$
Thus the surface is an \b[<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.