# Parametric Equations

Suppose we have two functions u = f(t) and v = g(t) defined on the same domain **D**. In this context we can call the variable t as the **parameter** and the equations
u = f(t)
v = g(t)
the **parametric equations**.

## Graph of Parametric Equations

In a given coordinate system the **graph** of the **parametric equations**
u = f(t)
v = g(t)
on their common domain **D** is the set of all the points (f(t), g(t)) for t in **D**.

Such a graph is also called the **parametric curve** represented by the given **parametric equations** or by the function
p(t) = (f(t), g(t)) for t in **D**
(Note that the range of p(t) is composed of ordered pairs. The graph of the parametric equations is **NOT** the graph of the function p(t) which is a three dimensional curve).

To be more descriptive when graphing **parametric equations** in the xy Cartesian coordinate system, it is customary to use x and y instead of f and g for the names of the functions and plot all the points
(x(t), y(t)) for t in **D**
The parametric curve can easily be plotted by using parametric grapher which also animates the parametric graphing process.

For graphing in the polar coordinate system r and θ are used instead of f and g for the names of the functions:
(r(t), θ(t)) for t in **D**
You can use polar parametric grapher which is the only known parametric grapher to plot parametric curves in the **polar coordinate system**.