Algebra and Trigonometry 10th Edition

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

Chapter 4 - Chapter Test - Page 355: 12

Answer

$(0,0)$ Vertices:$(h \pm a, k) =(\pm 1, 0)$ Foci: $(h \pm c, k) =(\pm \sqrt 5, 0)$
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Work Step by Step

The standard form of the equation of the hyperbola with a horizontal transverse axis can be expressed as: $\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$ The vertices and foci have the form $(\pm a, 0) $ and $(\pm c,0)$. The standard form of the equation of the hyperbola with a vertical transverse axis can be expressed as: $\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1$ The vertices and foci have the form $(0, \pm, a) $ and $(0, \pm c)$. The center is the midpoint of the vertices: $(0,0)$ We have: $ a=1; b=2$ $c=\sqrt {a^2+b^2}=\sqrt {1^2+2^2}=\sqrt 5$ and $\dfrac{x^2}{1^2}-\dfrac{y^2}{2^2}=1$ Vertices: $(h \pm a, k) =(\pm 1, 0)$ Foci: $(h \pm c, k) =(\pm \sqrt 5, 0)$
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