University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 10 - Section 10.6 - Conics in Polar Coordinates - Exercises - Page 591: 33

Answer

$\dfrac{1}{2+\cos \theta}$

Work Step by Step

The polar equation of a conic with eccentricity $e$ and directrix $x=k$ is defined as: $r=\dfrac{ke}{1+e \cos \theta}$ ...(1) We are given that the vertices are: $e=\dfrac{1}{2},k=1$ Then $x=1$ Thus, equation (1), becomes $r=\dfrac{(\dfrac{1}{2})}{1+(\dfrac{1}{2})\cos \theta}=\dfrac{1}{2+\cos \theta}$
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