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 671: 47

Answer

Foci: $(1, -3+\sqrt{3})$ and $(1, -3-\sqrt{3})$.

Work Step by Step

$\displaystyle \frac{(x-1)^{2}}{2}+\frac{(y+3)^{2}}{5}=1$ (major axis vertical), $a^{2}=5,$ $ a=\sqrt{5}\approx$2.236 $b^{2}=2$, $ b=\sqrt{2}\approx$1.414 Center: $(1, -3)$ $c^{2}=a^{2}-b^{2}=5-2=3$ $ c=\sqrt{3}\approx$1.732 Foci are $c$ units above and $c$ units below the center. Foci: $(1, -3+\sqrt{3})$ and $(1, -3-\sqrt{3})$.
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