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: 33



Work Step by Step

Major axis is horizontal. Equation of the ellipse: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ The ellipse passes through the point $(16,0)$ $\frac{16^2}{a^2}+\frac{0^2}{b^2}=1$ $16^2=a^2$ $a=16$ The ellipse passes through the point $(8,6)$ $\frac{8^2}{16^2}+\frac{6^2}{b^2}=1$ $\frac{1}{4}+\frac{6^2}{b^2}=1$ $\frac{36}{b^2}=1-\frac{1}{4}=\frac{3}{4}$ $3b^2=144$ $b^2=48$ $\frac{x^2}{16^2}+\frac{y^2}{48}=1$ $\frac{x^2}{256}+\frac{y^2}{48}=1$
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