Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 53


$$ r=\frac{4}{1+ \cos \theta} . $$

Work Step by Step

The polar equation of a conic of eccentricity $e \gt0$, with focus at the origin and directrix $x = d$ is $$ r=\frac{e d}{1+e \cos \theta}. $$ Now, since $e=1$ and $x=4$, then the polar equation is $$ r=\frac{4}{1+ \cos \theta} . $$
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