College Algebra (10th Edition)

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

Chapter 7 - Section 7.3 - The Ellipse - 7.3 Assess Your Understanding - Page 525: 18

Answer

Center at $(0,0).$ Vertices at $(\pm 3,0).$ Foci at $(\pm\sqrt{5},0)$

Work Step by Step

$\displaystyle \frac{x^{2}}{3^{2}}+\frac{y^{2}}{2^{2}}=1,\quad $axis along the x-axis (greater numerator under $x^{2}$) Apply the theorem: Equation of an Ellipse: Center at $(0,0);$ Major Axis along the $x$ -Axis An equation of the ellipse with center at $(0,0),$ foci at $(-c,0)$ and $(c,0),$ and vertices at $(-a,0)$ and $(a,0)$ is $\displaystyle \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\quad $ where $a \gt b \gt 0$ and $b^{2}=a^{2}-c^{2}$ The major axis is the x-axis. Center at $(0,0);$ Vertices at $(-a,0)=(-3,0)$ and $(a,0)=(3,0)$, Find c from $b^{2}=a^{2}-c^{2}$ $c^{2}=a^{2}-b^{2}$ $c^{2}=9-4$ $c=\sqrt{5}$ Foci : $(\pm\sqrt{5},0)$
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