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: 61


Polar equation: $r^2 \sin^2 \theta=4r \cos \theta$ or, $r^2=\dfrac{4\cos \theta}{\sin^2 \theta}$

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. $y=r \sin \theta$ Now, we have the equivalent Polar equation: $r^2 \sin^2 \theta=4r \cos \theta$ or, $r^2=\dfrac{4\cos \theta}{\sin^2 \theta}$
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