Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 10 - Analytic Geometry - 10.3 The Ellipse - 10.3 Assess Your Understanding - Page 657: 40



Work Step by Step

The ellipse has a major axis parallel to the y-axis, hence the equation of the ellipse here has the form $\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$, where $a\gt b\gt0$ and $(h,k)$ is the center. $(h,k)=(-1,-1)$, $a=2$, $b=1$, hence the equation is: $\frac{(x-(-1))^2}{1^2}+\frac{(y-(-1))^2}{2^2}=1\\(x+1)^2+\frac{(y+1)^2}{4}=1$
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