## Converting Parametric Curves to Cartesian

Parametric equations define a surface or a curve. If the equations define a curve in the plane, then and are expressed as functions of To convert the parametric equations to a single cartesian equation that relates and we must eliminate the parameter from the two equations. For example, if and then and so The parametric equation becomes the single cartesian equation Example: From the parametric equations find a cartesian equation that relates and Because there are and terms in the parametric equations, we look for an equation that relates and We can rearrange to give and to give hence Expanding and simplifying gives Example: From the parametric equations find a cartesian equation that relates and We can make the subject of the first equation and substitute it into the second. There is a slight complication hanging over from the parametric equation which is not visible in the cartesian equations. since we must be taking the square root of a non negative number, and If we consider the cartesian equation in isolation, we can substitute any value of We must have the condition inherited from the parametric equations that Example: From the parametric equations find a cartesian equation that relates and Because there are and terms in the parametric equations, we look for an equation that relates and We can rearrange to give and to give hence Expanding and simplifying gives #### Add comment Refresh