Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Preliminary Questions - Page 635: 3


The foci are $(0,\pm c)$.

Work Step by Step

The equation $$ \left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}=1 $$ is an ellipse. Since $a\lt b$, then $c=\sqrt{b^2-a^2}$ and the foci are $(0,\pm c)$.
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