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: 51


Vertices: $(0,±1)$ Eccentricity: $e=\frac{\sqrt 3}{2}$

Work Step by Step

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