In this section, the method for determining tangents and areas for curves that are described using parametric equations will be introduced.

When a curve is defined by the parametric equations,

     x = f(t) and y = g(t)

then the tangents of the curves are given by

           when     

From the above definition, it can be seen that the tangent is horizontal when (when) while it is vertical when (when).

The area under the curve described by the parametric equations

     x = f(t) and y = g(t) for a ≤ t ≤ b

is: