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: 38

Answer

Foci: $(1-\sqrt{7}, -2)$ and $(1+\sqrt{7},-2)$.
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Work Step by Step

$16 > 9$ so the major axis is horizontal. Comparing with $\displaystyle \frac{(x-h)^{2}}{a^{2}}+ \displaystyle \frac{(y-k)^{2}}{b^{2}}=1$, $a=4,$ $b=3$ Center: $(h,k)= (1, -2)$ Vertices: $(h-a, k),\quad (h+a, k) $ $(1-4, -2),\quad (1+4, -2)$ $(-3, -2),\quad (5, -2) $ Foci are $c$ units right and $c$ units left of center, $c^{2}=a^{2}-b^{2}16-9=7$ $c=\sqrt{7}\approx 2.65$ Foci: $(1-\sqrt{7}, -2)$ and $(1+\sqrt{7},-2)$.
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