Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 10 - Parametric Equations and Polar Coordinates - 10.3 Polar Coordinates - 10.3 - Page 707: 25

Answer

$$r=2 c \cos \theta$$

Work Step by Step

Since \begin{align*} x^{2}+y^{2}&=2 c x \\ r^{2}&=2 c r \cos \theta \\ r^{2}-2 c r \cos \theta&=0 \\ r(r-2 c \cos \theta)&=0 \end{align*} Then $ r=0$ or $r=2 c \cos \theta$ Since for $\theta=\frac{\pi}{2}+n \pi,$ $r=0$, then the curve is represented by $$r=2 c \cos \theta$$
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