16. Parametric Equations & Polar Coordinates

Graph the plane curve formed by the parametric equations and indicate its orientation.

$x\left(t\right)=-t+1$; $y\left(t\right)=t^2$

$-2\le t\le 2$

Graph the plane curve formed by the parametric equations and indicate its orientation.

$x\left(t\right)=2t-1$; $y\left(t\right)=2\sqrt{t}$

$t\ge 0$

Eliminate the parameter to rewrite the following as a rectangular equation.

$x\left(t\right)=2t-1$

$y\left(t\right)=t^5-2$

First eliminate the parameter, then graph the plane curve of the parametric equations.

$x\left(t\right)=2+\cos t$, $y\left(t\right)=-1+\sin t$; $0\le t\le2\pi$

Write parametric equations for the rectangular equation below.

$x^2+y^2=25$

11–14. Working with parametric equations Consider the following parametric equations.

a. Make a brief table of values of t, x, and y.

b. Plot the (x, y) pairs in the table and the complete parametric curve, indicating the positive orientation (the direction of increasing t).

x=2 t,y=3t−4;−10≤d≤10