Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 10 - Parametric Equations and Polar Coordinates - 10.6 Conic Sections in Polar Coordinates - 10.6 Exercise - Page 728: 8


$r= \frac{4}{1 - 2 cos (θ)}$

Work Step by Step

The directrix is r = -2sec(θ), so we need to convert this polar equation into cartesian form r cos(θ) = x, so multiply both sides by cos (θ) r cos(θ) = -2 x = -2 $r= \frac{ed}{1 - e cos (θ)}$ (cosine since directrix is vertical line, but negative since x =-2) e = 2, d=2 $r= \frac{ed}{1 - e cos (θ)}$ $r= \frac{(2) (2)}{1 - (2) cos (θ)}$ $r= \frac{4}{1 - 2 cos (θ)}$
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