College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 7 - Conic Sections - Exercise Set 7.1 - Page 670: 7

Answer

Foci: $(0, -4\sqrt{2})$ and $(0,4\sqrt{2}).$
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Work Step by Step

Major axis parallel to the $y$-axis, vertical. $a^{2}=81,$ $a=9$ $b^{2}=49,$ $b=7$ Vertices: $(h, k-a),\quad (h, k+a) $ $(0, -9),\quad (0, 9) $ Foci are $c$ units above and $c$ units below the center, $c^{2}=a^{2}-b^{2}=81-49=32$ $c=\sqrt{32}=4\sqrt{2}$ Foci: $(0, -4\sqrt{2})$ and $(0,4\sqrt{2}).$
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