College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 7 - Review Exercises - Page 540: 3


Ellipse. Center: $\quad (0,0)$ Vertices: $ \quad (0,5), \quad (0,-5)$ Foci: $\quad (0,3), \quad (0,-3)$

Work Step by Step

Both variables squared, a plus between terms$\Rightarrow$ Ellipse. Table 3: $\begin{array}{ll} {\text { Foci }}&{\text{Vertices}}&{\text{Equation}}\\\hline {(h, k+c)}&{(h,k+a)}&{\displaystyle \frac{(x-h)^{2}}{b^{2}}+\frac{(y-k)^{2}}{a^{2}}=1}\\ {(h,k-c)}&{(h,k-a)}&{a\gt b\gt 0\text{ and }b^{2}=a^{2}-c^{2}}\end{array}$ $a=5, \quad b=4$ Find$ \quad c$ : $c^{2}=a^{2}-b^{2}=25-16=9$ $c=3$ Center: $\quad (0,0)$ Vertices: $ \quad (h,k\pm a)=(0,\pm 5)$ Foci: $\quad (h,k\pm c)=(0,\pm 3)$
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