Calculus 8th Edition

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

Chapter 10 - Parametric Equations and Polar Coordinates - Review - Concept Check - Page 729: 9


a) See the explanation b) See the explanation. c) See the explanation.

Work Step by Step

a) Let us consider the points $A$ on the conic section, whose focus is $f$ and directrcix is $L$. Thus, the eccentricity$(e)$ can be calculated as: $e=\dfrac{|Af|}{|AL|}$; where, $\dfrac{|Af|}{|AL|}$ is a fixed ratio. b) For an ellipse: $e \lt 1$ For a hyperbola: $e \gt 1$ For a parabola: $e = 1$ c) For a conic section with eccentricity $(e)$ and directrx $x=d$, the polar equation can be represented as: $r=\dfrac{ed}{(1+e \cos \theta)}$; for directrix: $x=d$; $r=\dfrac{ed}{(1-e \cos \theta)}$; for directrix: $x=-d$; $r=\dfrac{ed}{(1+e \sin \theta)}$; for directrix: $y=d$; $r=\dfrac{ed}{(1-e \sin \theta)}$; for directrix: $y=-d$;
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.