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 636: 13


$$ \left(\frac{x}{40/3}\right)^{2}+\left(\frac{y}{50/3}\right)^{2}=1. $$

Work Step by Step

Since the foci are at $(0,\pm10)$ and $e=3/5$, then the foci are at the y-axis and $b\gt a$ $$\frac{3}{5}=\frac{10}{b}\Longrightarrow b=\frac{40}{3}$$ $$a^2=b^2-c^2=(\frac{50}{3})^2-100\Longrightarrow a=\frac{40}{3}$$ and hence the ellipse is centered at the origin and has the equation $$ \left(\frac{x}{40/3}\right)^{2}+\left(\frac{y}{50/3}\right)^{2}=1. $$
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