Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - 10.6 Exercises - Page 708: 4

Answer

$$r = \frac{9}{1 + 3\space cos(\theta)}$$

Work Step by Step

1. Determine the equation that we are going to use: Since the directrix is defined by $x = 3$, we are going to use $cos(\theta)$ in the formula. Since $3$ is positive, the equation will have "$+cos(\theta)$": $$r = \frac{ed}{1 + ecos(\theta)}$$ 2. Substitute the given values for $d$ (directrix) and e (eccentricity): $$r = \frac{(3)(3)}{1 + (3)cos(\theta)} = \frac{9}{1 + 3\space cos(\theta)}$$
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