unit hyperbola

The unit hyperbola (cf. the unit circle) is the special case


of the hyperbolaPlanetmathPlanetmath


where both the a and the b have equal to 1.  The unit hyperbola is rectangular, i.e. its asymptotes (y=±x) are at right anglesMathworldPlanetmathPlanetmath to each other.

The unit hyperbola has the well-known parametric


and also a trigonometric


The former yields the rational


when one substitutes  et=u, and the latter, via the substitutiontant2=u, the rational


(which does not give the left apex of the hyperbola).

Title unit hyperbola
Canonical name UnitHyperbola
Date of creation 2015-02-04 11:10:22
Last modified on 2015-02-04 11:10:22
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 24
Author pahio (2872)
Entry type Definition
Classification msc 51N20
Related topic HyperbolicFunctions
Related topic AreaFunctions
Related topic ConjugateHyperbola