Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 9 - Section 9.5 - Parametric Equations - Exercise Set - Page 1021: 72

Answer

Taking different values of t for both equations of x and y, the graph of the parametric equations can be plotted.

Work Step by Step

We know that the parametric equations are the equations having a common variable in both x and y. And by taking the values of t manually, one can get the values of x and y separately. And the corresponding points can be plotted to get a graph of the given parametric equations. For example: If the parametric equations are as given below: $\begin{align} & x=t \\ & y=2{{t}^{2}} \\ \end{align}$ Take the values of t manually and compute the values of x and y as given below: For $ t=1$ $\begin{align} & x=t \\ & =1 \end{align}$ $\begin{align} & y=2{{t}^{2}} \\ & =2{{\left( 1 \right)}^{2}} \\ & =2 \end{align}$ Similarly, for $ t=2$ $\begin{align} & x=t \\ & =2 \end{align}$ $\begin{align} & y=2{{t}^{2}} \\ & =2{{\left( 2 \right)}^{2}} \\ & =8 \end{align}$ And take some more values of t and get the values of x and y as given below: $\begin{align} & t=3 \\ & x=3 \\ & y=18 \\ \end{align}$ $\begin{align} & t=4 \\ & x=4 \\ & y=32 \\ \end{align}$ Thus, take these values of x and y to plot the graph as drawn below:
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