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 - Exercises - Page 635: 2


The vertices are $(\pm3,0)$ and $(0,\pm2)$. The foci are $(\pm \sqrt{5},0)$.

Work Step by Step

The equation $$ \left(\frac{x}{3}\right)^{2}+\left(\frac{y}{2}\right)^{2}=1. $$ is an ellipse. We have $a=3$, $b=2$, so $a\gt b$, $c=\sqrt{a^2-b^2}=\sqrt{5}$ and hence: The vertices are $(\pm3,0)$ and $(0,\pm2)$. The foci are $(\pm \sqrt{5},0)$.
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