The animation shows increasing portions of the same surface. This changes the visual appearannce of the paraboloid significantly.
Parabolic mirrors are used for their focussing properties. The animation changes roughly from the shape of a satellite antenna to the shape of a mirror of a front car light. — Telescope mirrors are even less curved.
Parabolic mirror with focussed rays, patch style rendered.
Parabolic mirror with focussed rays, anaglyph.
Anaglyph grid image of a parabolid.
Conic Section Surfaces
Hyperboloid of One Sheet
Hyperboloid of Two Sheet
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3DXM Surface Gallery