Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters."
For example, while the equation of a circle in Cartesian
coordinates can be given by 
, one set of parametric equations for the circle
are given by
 |  |  |
(1)
|
 |  |  |
(2)
|
illustrated above. Note that parametric representations are generally nonunique, so the same quantities may be expressed by a number of different parameterizations.
A single parameter is usually represented with the parameter 
, while the symbols 
and 
are commonly used for parametric equations in two parameters.
Parametric equations provide a convenient way to represent curves and surfaces, as implemented, for example, in the Wolfram
Language commands ParametricPlot[
x, y
, 
t, t1, t2
] and ParametricPlot3D[
x, y, z
, 
u, u1, u2
, 
v, v1, v2
]. Unsurprisingly, curves and surfaces obtained by way of parametric
equation representations are known as parametric
curves and parametric surfaces, respectively.
