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: 43

Answer

Vertices: $(±5,0)$ Eccentricity: $e=\frac{3}{5}$
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Work Step by Step

$\frac{x^2}{25}+\frac{y^2}{16}=1$ $\frac{x^2}{5^2}+\frac{y^2}{4^2}=1$ The major axis is horizontal. Standard form when major axis is horizontal: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ So: $a=5$ and $b=4$ $a^2=b^2+c^2$ $c^2=a^2-b^2=25-16=9$ $c=3$ $e=\frac{c}{a}=\frac{3}{5}$ Vertices when major axis is horizontal: $(±a,0)=(±5,0)$
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