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 x1
and the corresponding y equation is named y1
. 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.