Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 11 - Section 11.6 - Polar Equations of Conics - 11.6 Exercises - Page 831: 46

Answer

See explanations.

Work Step by Step

Step 1. The standard form of a conic polar equation is $r=\frac{ed}{1\pm e\cdot cos\theta}$ or $r=\frac{ed}{1\pm e\cdot sin\theta}$. Step 2. As the focus is at the pole, any point $P(r_p, \theta_p)$ on the curve will have a distance to the pole as $|r_p|$ Step 3. We conclude that the distance from that focus to any point $P(r_p, \theta_p)$ on the conic is $|r_p|$.
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