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: 2

Answer

$ x=-\sqrt{y}$

Work Step by Step

Express t in terms of one variable and substitute it into the other equation. $y=t\Rightarrow\quad t=y$ $x=-\sqrt{t} \Rightarrow\quad \fbox{$ x=-\sqrt{y} $}$ 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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