Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 9 - Section 9.6 - Conic Sections in Polar Coordinates - Exercise Set - Page 1032: 50

Answer

ellipse, see graph
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Work Step by Step

Step 1. Rewrite the equation as $r=\frac{4/cos\theta}{2/cos\theta-1}=\frac{4}{2-cos\theta}=\frac{2}{1-\frac{1}{2}cos\theta}$ Step 2. We can identify $e=\frac{1}{2}\lt 1$ and the conic is an ellipse with $ep=2, p=4$ and directrix as $x=-4$ Step 3. We can graph the equation as shown in the figure.
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