Chapter 9, Problem 9CT

To determine

To graph: the curve represented by the parametric equation.

Explanation of Solution

Given information:

The parametric equations are $x=e^{-t},y=2e^t$ .

Graph: to draw the graph, first substitute the value of $t$ in the interval and then find the corresponding $\left(x,y\right)$ ,

$t$	$x$	$y$
$-1$	$e$	$\frac{2}{e}$
$0$	$1$	$2$
$1$	$\frac{1}{e}$	$2e$

By plot these pairs and join them, the graph can be obtained as:

  

Interpretation: from the above graph it can be observed that the rectangular equation is $y=\frac{2}{x},x>0$ .