Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 4 - 4.4 - Translations of Conics - 4.4 Exercises - Page 348: 45

Answer

Center: $(1,5)$ Foci: $(1,9)~~and~~(1,1)$ Vertices: $(1,10)~~and~~(1,5-5)=(1,0)$
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Work Step by Step

The standard form of the equation of the elipse when the major axis is: - horizontal: $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ in which $(h,k)$ is the center and $2a$ is the major axis length and $2b$ is the minor axis length. - vertical: $\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$ in which $(h,k)$ is the center and $2a$ is the major axis length and $2b$ is the minor axis length. $\frac{(x-1)^2}{9}+\frac{(y-5)^2}{25}=1$ $\frac{(x-1)^2}{3^2}+\frac{(y-5)^2}{5^2}=1$ $a=5,~~b=3$ $c^2=a^2-b^2=25-9=16$ $c=4$ Center: $(1,5)$ The major axis is vertical: - the foci: $(1,5+4)=(1,9)~~and~~(1,5-4)=(1,1)$ - the vertices: $(1,5+5)=(1,10)~~and~~(1,5-5)=(1,0)$
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