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 1031: 41

Answer

hyperbola, see graph
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Work Step by Step

Step 1. Rewrite the given equation in standard form as $r=\frac{12}{4+5sin\theta}=\frac{3}{1+\frac{5}{4}sin\theta}$ Step 2. We can identify: $e=\frac{5}{4}\gt 1$, representing a hyperbola. Step 3. We can identify: $ep=3, p=\frac{12}{5}$ and the directrix as $y=\frac{12}{5}$ Step 4. We can graph the equation as shown in the figure.
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