Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - 10.3 Exercises - Page 687: 28

Answer

a. Cartesian, $(x-2)^{2}+(y -3)^{2}=5^{2}$. b. Polar, $r=4$.

Work Step by Step

$a.$ The Cartesian equation here is $(x-2)^{2}+(y -3)^{2}=5^{2}$. When the center is not at the origin, the polar equation will be harder to derive, since both r and $\theta$ vary from point to point. $b.$ When the center is at the origin, the polar equation is $r=4,$ which is as simple as it gets. The Cartesian is not too difficult, $x^{2}+y^{2}=4^{2}$, but the polar form is far simpler.
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