Hyperbolic cylinder
= Hyperbolic cylinder
{title2=$u^2/a^2-v^2/b^2=1$}
For $a,b>0$, this <quadric surface> is independent of its third coordinate and is formed by translating a <hyperbola> along that direction. Its two connected components correspond to $u\geq a$ and $u\leq-a$. In <elliptic cylindrical coordinates>, fixing a generic angular coordinate selects a half-branch of such a cylinder because the signs of both planar coordinates are fixed by that angular value.