A parametric equation is a type of

equation used in

graphing. Just as there are

function equations and

polar equations, there are parametric equations. The special thing about parametric equations is that they show the graph of a function over time. This has many practical applications, such as seeing the relative positions of different objects at a certain point in time. Instead of the x variable of functions or the theta variable of polar equations, the variable in parametric equations is

__t__, and it represents time.

There are two parts to a parametric equation: the x equation and the y equation. The x equation determines what the x

coordinate of the point graphed for each time

__t__, and the y equation does likewise for the y coordinate. As a rule of thumb, the first x equation is named x

_{1} and the corresponding y equation is named y

_{1}. When you put both of these together for each value of

__t__ that you are graphing, you come up with the graph of the equation. It is a bit difficult to visualize the result of these equations unless you have had a bit of experience with graphing, but if you mess around with the parametric graphing feature of a

graphing calculator for a while, it becomes easier to figure out what the equations mean.