# Article

# Article

- Mathematics
- Geometry
- Parametric equation

- Mathematics
- Analysis (calculus)
- Parametric equation

# Parametric equation

Article By:

**Taylor, Angus E. **Department of Mathematics, University of California, Berkeley, California.

Last reviewed:August 2019

DOI:https://doi.org/10.1036/1097-8542.488000

**A type of mathematical equation used, typically, to represent curves in a plane or in space of three dimensions.** In principle, however, there is no limitation to any particular number of dimensions. A parameter is actually an independent variable. In elementary analytic geometry a curve in the *xy* plane is often studied, in the first instance, as the locus of an equation *y* = *F*(*x*) or *G*(*x*, *y*) = 0. The form *y* = *F*(*x*) is not adequate for the complete representation of certain curves, whereas the form *G*(*x*,*y*) = 0 may be adequate. The circle *x*^{2} + *y*^{2} − 16 = 0 affords an example. But the form *G*(*x*,*y*) = 0 is not always convenient. The parametric form *x* = *f*(*t*), *y* = *g*(*t*) is often the most convenient; it is often the naturally occurring form of representation of the curve. For the circle *x*^{2} + *y*^{2} − 16 = 0, one possible parametric representation is *x* = 4 cos *t* and *y* = 4 sin *t*.

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