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## Main Question or Discussion Point

Hello!

In vector valued functions, I don't know how to find a curve's cartesian equation by inspecting its parametric ones...

For example I know from a worked example that if [tex]f: R^2 \rightarrow R[/tex] is given by f(x,y) = xy, and [tex]r(t) = \left[\begin{array}{ccccc} sin(t) \\ cos(t) \end{array}\right][/tex], then the Cartesian equation for this curve r is:

But what if we had [tex]f: R^2 \rightarrow R[/tex] is given by f(x,y) = x

How do can I try to find its Cartesian equation?

In vector valued functions, I don't know how to find a curve's cartesian equation by inspecting its parametric ones...

For example I know from a worked example that if [tex]f: R^2 \rightarrow R[/tex] is given by f(x,y) = xy, and [tex]r(t) = \left[\begin{array}{ccccc} sin(t) \\ cos(t) \end{array}\right][/tex], then the Cartesian equation for this curve r is:

**x**(which is just the unit circle).^{2}+y^{2}=1But what if we had [tex]f: R^2 \rightarrow R[/tex] is given by f(x,y) = x

^{2}y, and [tex]r(t) = \left[\begin{array}{ccccc} sin(t) \\ cos^2(t) \end{array}\right][/tex], ([tex]t \in [0, \pi/2[/tex])?How do can I try to find its Cartesian equation?