Chapter 9, Problem 62CR

a.

To determine

To graph the curve represented by the parametric equation and indicate its orientation.

Explanation of Solution

Given information:

The given parametric equation is

  $\begin{array}{l}x=5t\\ y=t^2\end{array}$

Graph:

Make the table of values

t	0	1	$-1$	2
x	0	5	$-5$	10
y	0	1	1	4

The graph of the parametric equation.

  

Interpretation: the orientation of the graph is $y=\frac{x^2}{25}$

b.

To determine

To eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Answer to Problem 62CR

The required rectangular equation is $y=\frac{x^2}{25}$

Explanation of Solution

Given information:

The given parametric equation is

  $\begin{array}{l}x=5t\\ y=t^2\end{array}$

Calculation:

Evaluate t in terms of x

  $\begin{array}{l}x=5t\\ t=\frac{x}{5}\\ \text{substitute }t\text{ in second equation}\\ y={\left(\frac{x}{5}\right)}^2\\ y=\frac{x^2}{25}\end{array}$

The required rectangular equation is $y=\frac{x^2}{25}$