Category:Definitions/Elliptical Paraboloids

This category contains definitions related to Elliptical Paraboloids.
Related results can be found in Category:Elliptical Paraboloids.

Definition 1

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.

Definition 2

An elliptical paraboloid is a paraboloid which can be embedded in a Cartesian $3$-space and described by the equation:

$\dfrac {y^2} {b^2} + \dfrac {z^2} {c^2} = 2 a x$