Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 10 - Analytic Geometry - 10.6 Polar Equations of Conics - 10.6 Assess Your Understanding - Page 685: 45


Use the fact that $d(F,P)=e\cdot d(D,P)$ and that $d(D,P)=p+r\sin\theta$ to derive and have $r=\dfrac{ep}{1-e\sin\theta}$ Refer to the step-bystep part for the actual derivation.

Work Step by Step

We know that $d(F,P)=e\cdot d(D,P)$ and that $d(D,P)=p+r\sin\theta$. Hence, $r=e\cdot(p+r\sin\theta)\\r=ep+er\sin\theta\\r-er\sin\theta=ep\\r(1-e\sin\theta)=ep\\r=\frac{ep}{1-e\sin\theta}$
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