University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 10 - Section 10.3 - Polar Coordinates - Exercises - Page 577: 36


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

Work Step by Step

Conversion of polar coordinates and Cartesian coordinates are as follows: a)$r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$ b) $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$ c) $x=r \cos \theta$, d) $y=r \sin \theta$ Since, $r^2=x^2+y^2$, and $y=r \sin \theta$ , therefore the Cartesian equation is $x^2+y^2=4y$ This can be re-written as: $x^2+y^2=4y \implies x^2+(y-2)^2=4$ This shows a circle centered at the points (0,2) with radius $2$.
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