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 347: 1

Answer

(b) $\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$

Work Step by Step

Remember that hyperbolas follow the general equations: $\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$ or $\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1$ The transverse axis is along whichever component is positive. So, in this case the $x^2$ term needs to be positive. Thus, (b) $\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$ is a hyperbola with a horizontal transverse axis.
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