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: 37

Answer

Foci: $(2-\sqrt{5},1)$ and $(2+\sqrt{5},1)$.

Work Step by Step

$9 > 4$ so the major axis is horizontal. Comparing with $\displaystyle \frac{(x-h)^{2}}{a^{2}}+ \displaystyle \frac{(y-k)^{2}}{b^{2}}=1$, $a=3,$ $b=2$ Center: $(h,k)= (2, 1)$ Vertices: $(h-a, k),\quad (h+a, k) $ $(2-3, 1),\quad (2+3, 1)$ $(-1,1),\quad (5,1) $ Foci are $c$ units right and $c$ units left of center, $c^{2}=a^{2}-b^{2}=9-4=5$ $ c=\sqrt{5}\approx$2.236 Foci: $(2-\sqrt{5},1)$ and $(2+\sqrt{5},1)$.
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