Parametric equations use one or more parameters to represent a curve or surface, while Cartesian equations use x and y coordinates to represent a curve or surface.
To convert a parametric equation to a Cartesian equation, you can use the substitution method. Substitute the parameter in the parametric equation with the equivalent expression in terms of x and y.
Parametric equations can provide a more efficient way to represent certain curves and surfaces, as they often require fewer terms compared to their Cartesian counterparts. They can also allow for easier visualization and manipulation of complex shapes.
Yes, parametric equations can represent all types of curves and surfaces that can be represented by Cartesian equations. However, certain curves and surfaces may be easier to represent using one form over the other.
To graph a parametric equation, you can create a table of values by choosing values for the parameter and calculating the corresponding x and y values. Then, plot these points on a graph and connect them to create the curve or surface.