The above circle was graphed using parametric equations. Parametric equations give you the ability to graph non-function relationships by writing each of your relationship's variables as functions of a new parameter.
Here are the parametric equations used above: 
and 
.
With a little algebra we can see that these equations collapse into the
equation we are used to seeing for a circle of radius 1 centered at the
origin: 
.
Now for the fun part--manipulating these parametric equations to produce different kinds of graphs.
A simple maneuver is to multiply each equation by two:
As you can see this changes the radius of the circle to two.
Adding or subtracting from the equations has the expected translating effect:
and 
Notice however, that this translation is more intuitive than the usual equation of a circle translation. Adding two to x moves it two to the right--subtracting 1 fromm y moves it down 1. This is a nice benefit of parametric equations.