Generating a Hyperboloid by Rotating a Line

rotation angle θ

0

static angle ϕ

30

A hyperboloid can be generated by rotating a line around the

z

axis. The vertical line through the origin is first translated in the

x

-

y

plane and then rotated about an axis in the

x

-

y

plane. Enough information is then available to use standard equations to calculate the foci and hyperbola curves; two foci are shown as small spheres.