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: 54



Work Step by Step

Major axis is vertical. $(0,±8)=(0,±a)$ $a=8$ $e=\frac{c}{a}$ $\frac{1}{2}=\frac{c}{8}$ $2c=8$ $c=4$ $a^2=b^2+c^2$ $b^2=a^2-c^2=8^2-4^2=64-16=48$ $b=4\sqrt 3$ Standard form when major axis is vertical: $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ $\frac{x^2}{(4\sqrt 3)^2}+\frac{y^2}{8^2}=1$ $\frac{x^2}{48}+\frac{y^2}{64}=1$
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