Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 9 Quadratic Relations and Conic Sections - 9.4 Graph and Write Equations of Ellipses - 9.4 Exercises - Problem Solving - Page 638: 49

Answer

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Work Step by Step

The standard form of an ellipse is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ where $a$ is half the total width and $b$ is a length of the minor axis. Plugging in $a=\frac{110}{2}=55\\b=\frac{135}{2}=67.5$ for the smallest value we get: $$\frac{x^2}{55^2}+\frac{y^2}{67.5^2}=1$$ Plugging in $a=\frac{155}{2}=77.5\\b=\frac{185}{2}=92.5$ for the largest value we get: $$\frac{x^2}{77.5^2}+\frac{y^2}{92.5^2}=1$$ The area of an ellipse is $V=\pi ab$ Obtain $\pi(55)(67.5) \leq A \leq \pi (77.5)(92.5)\\3712.5 \pi \leq A\leq7168.75 \pi\\11663.2 \leq A \leq 22521.3$
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