Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 4 - 4.3 - Conics - 4.3 Exercises - Page 338: 48


Vertices: $(0,±8)$ Eccentricity: $e=\frac{3}{4}$

Work Step by Step

$16x^2+7y^2=448$ $\frac{x^2}{28}+\frac{y^2}{64}=1$ $\frac{x^2}{(2\sqrt 7)^2}+\frac{y^2}{8^2}=1$ The major axis is vertical. Standard form when major axis is vertical: $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ So: $a=8$ and $b=2\sqrt 7$ $a^2=b^2+c^2$ $c^2=a^2-b^2=64-28=36$ $c=6$ $e=\frac{c}{a}=\frac{6}{8}=\frac{3}{4}$ Vertices when major axis is horizontal: $(0,±a)=(0,±8)$
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