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: 58


The conic section is an ellipse with $e=3/4$ and directrix $x=4$.

Work Step by Step

Converting the given equation to the standard form $$ r=\frac{e d}{1+e \cos \theta}. $$ We get $$ r=\frac{12}{4+ 3\cos \theta}=\frac{3}{1+(3/4) \cos \theta}. $$ Then we have $ ed=3, e=\frac{3}{4} .$ Thus, $d=4$ and the directrix equation is $x=4$. Since $e\lt 1$, then the conic section is an ellipse.
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