Rotating a line in 3D gives a... hyperbola?

Rotate a line about the z-axis and trace the intersection with the plane y=0[br][br]Original animated GIF here which is even more cool![br][url=http://twitter.com/DrTrapezio/status/700787251723112448]twitter.com/DrTrapezio/status/700787251723112448[/url][br][url=http://www.gifbin.com/988980]gifbin.com/988980[/url]

Information: Rotating a line in 3D gives a... hyperbola?