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: 55


The thumbtacks: $(±\sqrt 5,0)~ft$ The length of the string $=2\sqrt 5~ft$

Work Step by Step

The major axis is horizontal. The major axis is equal to the width of 6 feet: $2a=6$ $a=3$ The half of the minor axis is equal to the height of 2 feet: $b=2$ $a^2=b^2+c^2$ $c^2=a^2-b^2=3^2-2^2=5$ $c=\sqrt 5$ The thumbtacks must be placed at the foci. When major axis is horizontal: $(±c,0)=(±\sqrt 5,0)$ The length of the string is equal to $2c=2\sqrt 5$
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