Definition:Paraboloid

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Definition

A paraboloid is a figure whose sections parallel to at least one plane are parabolas.


Elliptical Paraboloid

Let $\PP$ be a paraboloid.

Let $P_1$ and $P_2$ be two plane sections of $\PP$ such that both $P_1$ and $P_2$ are parabolas.

Let $P_3$ be a plane section of $\PP$ perpendicular to both $P_1$ and $P_2$.


Then $\PP$ is an elliptical paraboloid if and only if $P_3$ is an ellipse.


Hyperbolic Paraboloid

Definition:Paraboloid/Hyperbolic

Circular Paraboloid

A circular paraboloid is a surface of revolution obtained by revolving a parabola around its axis.


Also see

  • Results about paraboloids can be found here.


Sources