The graphs of parametric equations depend on the values of all the different variables, so we will experiment with these variables and explore how their effect on the graphs of the equations. For example, in the following equation, what happens when a and b are varied and t is between 0 and

Click here to see the graph change as the value of a is varied.

Click here to see the graph change as the value of b is varied.

Now, what would happen if we allow t to vary beyond ? Let's allow t to go all the way to 100 and see what kinds of graphs we get when a and b are equal to each other.

Click here to see some of the more interesting graphs where t is varied.