Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 10 - Section 10.2 - The Ellipse - Exercise Set - Page 777: 18



Work Step by Step

Standard equation for ellipse for horizontal major axis is:$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$ Standard equation for ellipse for vertical major axis is:$\dfrac{(x-h)^2}{b^2}+\dfrac{(y-k)^2}{a^2}=1$ Here, $(h,k)$ represents center with foci $c$ and $c^2=a^2-b^2$ Since, we can be found from the given graph that center is (0,0) for horizontal major axis, we have $a=4, b=2$ This, the equation of ellipse is: $\dfrac{x^2}{4^2}+\dfrac{y^2}{2^2}=1$ or, $\dfrac{x^2}{16}+\dfrac{y^2}{4}=1$
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