Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 10 - Analytic Geometry - 10.2 Ellipses - 10.2 Exercises - Page 979: 42

Answer

$e=\dfrac{2}{\sqrt 8} \approx 0.71$

Work Step by Step

The standard form of an ellipse can be written as: $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1....(1); $and has foci $( \pm c, 0)$ where ; $c^2=a^2-b^2$. On comparison, we have $a=\sqrt 8$ and $b=2$. Now, $c^2=a^2-b^2 \implies c^2 =(\sqrt 8)^2-(2)^2 \implies c^2= 4$ or, $c=2$ The eccentricity of the ellipse can be found as: $e=\dfrac{c}{a}$ Therefore, $e=\dfrac{2}{\sqrt 8} \approx 0.71$
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