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 11.3 - Polar Coordinates - Exercises 11.3 - Page 663: 36


A circle center at the points $(0,2)$ with radius $2$.

Work Step by Step

The conversion of polar coordinates and Cartesian coordinates are described as follows: 1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$ 2. $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$ 3. $x=r \cos \theta$ and 4. $y=r \sin \theta$ As we know that $r^2=x^2+y^2$, and $y=r \sin \theta$ , Thus, the Cartesian equation is $x^2+y^2=4y$ $\implies x^2+y^2=4y$ or, $x^2+(y-2)^2=4$ Hence, this shows a circle center at the points $(0,2)$ with radius $2$.
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