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 is 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.
The symbol 
is commonly used for a single 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.
