Solution
= Solution
Let $\lambda_1=\lambda_2=\lambda>0$ and $\lambda_3=-\gamma<0$. Then
$$
\frac{x_1'^2+x_2'^2}{k/\lambda}-\frac{x_3'^2}{k/\gamma}=1.
$$
This is a \b[<one-sheet hyperboloid> of revolution] around the $x_3'$ axis. Its circular waist has radius $\sqrt{k/\lambda}$ at $x_3'=0$, and its radius grows with $|x_3'|$. In the original coordinates the axis is the <eigenvector> direction belonging to the negative <eigenvalue>.