Chapter 8.4, Problem 39E

To determine

To draw: the curve given by the parametric equations.

Answer to Problem 39E

  

Explanation of Solution

Given: $x=\frac{3t}{1+t^3},y=\frac{3t}{1+t^3}$

Calculation:

Sketch the curve given by parametric equation $x=\frac{3t}{1+t^3}$ and $y=\frac{3t^2}{1+t^3}$

To draw the graph, put various values of $t$ and find the corresponding values of $x$ and $y$ .

On tabulating the results,

$t$	$-1.5$	$-1$	$-0.5$	$0$	$0.5$	$1$	$1.5$	$2$
$x$	$1.894$	$\infty$	$-1.714$	$0$	$1.33$	$1.5$	$1.028$	$0.66$
$y$	$-2.84$	$\infty$	$0.857$	$0$	$0.66$	$1.5$	$1.54$	$1.33$

Using the table, get the following graph of the parametric equations $x=\frac{3t}{1+t^3}$ and $y=\frac{3t^2}{1+t^3}$ .

  

Conclusion:

Therefore, the required graph is drawn.