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In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point, in which case, the parameter is often, but not necessarily, time, and the point describes a curve, called a parametric curve. In the case of two parameters, the point describes a surface, called a parametric surface.
Such a parametric equation completely determines the curve, without the need of any interpretation of t as time, and is thus called a parametric equation of the curve (this is sometimes abbreviated by saying that one has a parametric curve). One similarly gets the parametric equation of a surface by considering functions of two parameters t and u.
In calculus, a parametric derivative is a derivative of a dependent variable with respect to another dependent variable that is taken when both variables depend on an independent third variable, usually thought of as "time" (that is, when the dependent variables are x and y and are given by parametric equations in t).
A parametric surface is a surface in the Euclidean space which is defined by a parametric equation with two parameters :. Parametric representation is a very general way to specify a surface, as well as implicit representation .
Parametric equation, a representation of a curve through equations, as functions of a variable; Parametric statistics, a branch of statistics that assumes data has come from a type of probability distribution; Parametric derivative, a type of derivative in calculus
A parametric equation for a curve expresses the coordinates of the points of the curve as functions of a variable, called a parameter. [8] [9] For example, = = are parametric equations for the unit circle, where t is the parameter. Together, these equations are called a parametric representation of the curve.
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The Fermat spiral with polar equation = can be converted to the Cartesian coordinates (x, y) by using the standard conversion formulas x = r cos φ and y = r sin φ.Using the polar equation for the spiral to eliminate r from these conversions produces parametric equations for one branch of the curve: