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: 4

Answer

The foci are located at $(0, -\sqrt{33})$ and $(0, \sqrt{33})$
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Work Step by Step

Major axis parallel to the $y$-axis, vertical. $a^{2}=49,$ $a=7$ $b^{2}=16,$ $b=4$ Vertices: $(h, k-a),\quad (h, k+a) $ $(0, -7),\quad (0, 7) $ Foci are $c$ units above and $c$ units below the center, $c^{2}=a^{2}-b^{2}=49-16=33$ $c=\sqrt{33}$ The foci are located at $(0, -\sqrt{33})$ and $(0, \sqrt{33})$
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