Definition:Elliptical Paraboloid/Definition 2

Definition

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

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

In this orientation:

the plane sections of $\PP$ parallel to the $x$-$y$ plane and the $x$-$z$ plane are parabolas

the plane sections of $\PP$ parallel to the $y$-$z$ plane are ellipses.

Also presented as

The equation defining an elliptical paraboloid embedded in a Cartesian $3$-space can also be presented in the form:

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

Also see

• Equivalence of Definitions of Elliptical Paraboloid

• Results about elliptical paraboloids can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): paraboloid
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): paraboloid