College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 7, Conic Sections - Section 7.2 - Ellipses - 7.2 Exercises - Page 563: 52

Answer

$\frac{x^2}{25}+\frac{y^2}{50}=1$

Work Step by Step

Minor axis: $Length=2b$ $2=10$ $b=5$ Foci on y-axis: major axis is vertical. Use the point $(\sqrt 5,\sqrt {40})$. Equation of the ellipse: $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ $\frac{(\sqrt 5)^2}{5^2}+\frac{(\sqrt {40})^2}{a^2}=1$ $\frac{1}{5}+\frac{40}{a^2}=1$ $\frac{40}{a^2}=1-\frac{1}{5}=\frac{4}{5}$ $4a^2=200$ $a^2=50$ $a=5\sqrt 2$ $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ $\frac{x^2}{5^2}+\frac{y^2}{(5\sqrt 2)^2}=1$ $\frac{x^2}{25}+\frac{y^2}{50}=1$
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