Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 10 - Section 10.6 - Conic Sections in Polar Coordinates - 10.6 Exercises - Page 688: 8


$r= \dfrac{4}{1 - 2 \cos (θ)}$

Work Step by Step

Convert the polar equation into Cartesian form: The directrix is $r = -2sec(θ)$ or, $r cos(θ) = x$ Now, multiply both sides by $\cos θ$. we have $r \cosθ = -2 \implies x = -2$ since the directrix is a vertical line, we have $r= \dfrac{ed}{1 - e \cos (θ)}$ and $ x =-2$ Given: $e = 2, d=2$ Now, we have $r= \dfrac{ed}{1 - e \cos (θ)}= \dfrac{(2) (2)}{1 - (2) \cos θ}$ Hence, $r= \dfrac{4}{1 - 2 \cos θ}$
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