How does graphing the x=t equation help you determine the rectangular domain restrictions for a set of parametric equations.

Question

Give a good explanation please.

Answer 1

I think that you're asking how "Sketching a plane curve" helps determine the domain and range for x and y. If so, I hope this helps!

A really cool thing about parametric equations is that they model things that aren't typical functions of y on a rectangular plane. It's difficult, just looking at the equations and restrictions given in a parametric problem, to determine what the rectangular graph will look like. I can't figure out how to attach pictures here, so try this video by Patrick JMT. I think he demonstrates what I mean: https://youtu.be/tsnHL1Lb5MU

You should make a table, starting with possible values for t, to find the corresponding x and y coordinates. Graphing those in order of t shows you where your equations exist on the Cartesian/rectangular plane.

I hope this helps! Parametric equations are awesome!

-Liz Z.