Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 11: Parametric Equations and Polar Coordinates - Section 11.1 - Parametrizations of Plane Curves - Exercises 11.1 - Page 647: 1

Answer

$y=x^{2}$

Work Step by Step

Express $t$ in terms of one variable and substitute it into the other equation. $x=3t\displaystyle \Rightarrow\quad t=\frac{x}{3}$ $y=9t^{2} \displaystyle \Rightarrow\quad y=9(\frac{x}{3})^{2}=x^{2}\qquad $\fbox{$y=x^{2}$} To graph, create a table using several values for t, and then calculate $(x(t), y(t)),$ plotting the points as you go. Join with a smooth curve, noting the direction in which t increases.
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