Introduction to Parametric Equations

In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both [latex]x[/latex] and [latex]y[/latex] depend on, and as the parameter increases, the values of [latex]x[/latex] and [latex]y[/latex] trace out a path along a plane curve. For example, if the parameter is [latex]t[/latex] (a common choice), then [latex]t[/latex] might represent time. Then [latex]x[/latex] and [latex]y[/latex] are defined as functions of time, and [latex]\left(x\left(t\right),y\left(t\right)\right)[/latex] can describe the position in the plane of a given object as it moves along a curved path.