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: 50


Vertices: $(0,±\sqrt 5)$ Eccentricity: $e=\frac{\sqrt 5}{5}$

Work Step by Step

$5x^2+4y^2=20$ $\frac{x^2}{4}+\frac{y^2}{5}=1$ $\frac{x^2}{2^2}+\frac{y^2}{(\sqrt 5)^2}=1$ The major axis is vertical. Standard form when major axis is vertical: $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ So: $a=\sqrt 5$ and $b=2$ $a^2=b^2+c^2$ $c^2=a^2-b^2=5-4=1$ $c=1$ $e=\frac{c}{a}=\frac{1}{\sqrt 5}=\frac{\sqrt 5}{5}$ Vertices when major axis is horizontal: $(0,±a)=(0,±\sqrt 5)$
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