Definition:Hyperbolic Paraboloid/Definition 2

Definition

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

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

In this orientation:

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

the plane sections of $\PP$ parallel to the $x$-$y$ plane are hyperbolas.

Also presented as

The equation defining a hyperbolic 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 Hyperbolic Paraboloid

• Results about hyperbolic 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