Lesson 15 Preview: Parametric Equations
- Author:
- Will McGuffey, Ken Schwartz
Parametric Equations
There are many graphs in the plane that are not graphs of functions because they do not pass the vertical line test (e.g., a circle or sideways parabola). But what if we imagine a point moving along the curve? Then, it's position is a function of time (because you can't be in two places at once).
If (x,y) is a point moving along a curve, we can parameterize its coordinates. That means we can define each coordinate individually as a function of time: and are both functions of time. So, the coordinate of the point are .
Interact with the applet below which shows two parametrized "curves" (red and blue). Think of as time so that means that we are looking at the motion of a point during the first five seconds of motion. The curve starts at an initial point and ends at a terminal point.