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: 55


The conic section is a hyperbola. directrix: $x=2$ eccentricity: $e=4$

Work Step by Step

Comparing the given equation with the standard form $$ r=\frac{e d}{1+e \cos \theta}. $$ We get $$ed=8, e=4.$$ We solve for $d$: $d=\frac{8}{4}=2$ Thus, we see that the directrix is: $x=2$ Since $e\gt 1$, then the conic section is a hyperbola.
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