A parametric representation of a curve is not unique. That is, a curve C may be represented by two (or more) different pairs of parametric equations.

Are parameterized equations unique?

Parametric equations are commonly used in kinematics, where the trajectory of an object is represented by equations depending on time as the parameter. ... Parameterizations are non-unique; more than one set of parametric equations can specify the same curve.

What is the purpose of parametric equations?

Parametric equations can be used to describe all types of curves that can be represented on a plane but are most often used in situations where curves on a Cartesian plane cannot be described by functions (e.g., when a curve crosses itself).