Lesson 15 Preview: Parametric Equations

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 [b]imagine a point moving along the curve[/b]? Then, it's [b]position [/b]is a function of [b]time [/b](because you can't be in two places at once). [br][br]If (x,y) is a point moving along a curve, we can [b]parameterize [/b]its coordinates. That means we can define each coordinate individually as a function of time: [math]x=x\left(t\right)[/math] and [math]y=y(t)[/math] are both functions of time. So, the coordinate of the point are [math](x(t),y(t))[/math]. [br][br]Interact with the applet below which shows two parametrized "curves" (red and blue). Think of [math]t[/math] as time so that [math]0\le t\le5[/math] means that we are looking at the motion of a point during the first five seconds of motion. The curve starts at an [b]initial point[/b] and ends at a [b]terminal point[/b].

Information: Lesson 15 Preview: Parametric Equations