Parametric Equations for a Hyperbola

t

0.00001

asymptotes

distances

switch x and y

A hyperbola in the

x

-

y

plane may be drawn by making use of a parametric representation involving the secant and tangent. The example in this Demonstration plots the equations

x(t)=3sect

,

y(t)=4tant

(or, switching

x

and

y

,

x(t)=4tant

,

y(t)=3sect

). Graphs of

x(t)

,

y(t)

and the hyperbola are shown.

External Links

Hyperbola (Wolfram MathWorld)

Parametric Equations (Wolfram MathWorld)

Conic Sections: Polar Equations

Illustrating Secant with the Unit Circle

Illustrating Tangent with the Unit Circle

Permanent Citation

Abby Brown

"Parametric Equations for a Hyperbola"
http://demonstrations.wolfram.com/ParametricEquationsForAHyperbola/
Wolfram Demonstrations Project
Published: December 10, 2018