Calculus 8th Edition

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

Chapter 10 - Parametric Equations and Polar Coordinates - Review - Exercises - Page 731: 45

Answer

Vertices: $( \pm 3, 0)$ and Foci: $(\pm 1,0)$
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Work Step by Step

The equation is: $ \frac{x^2}{9}+\frac{y^2}{8}=1$ The standard form of the equation of an ellipse with center $(h,k)$ with major axis and minor axis of lengths $2a$ and $2b$ is defined as: $ \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ or, $ \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$ Compare the given equation with the standard form, we get $a=3$ and $b=2 \sqrt2$ and $c^2= a^2-b^2=3-2 \sqrt2$ or, $c=1$ Vertices: $( \pm 3, 0)$ and Foci: $(\pm 1,0)$ See the attached graph.
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