## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 4 - 4.4 - Translations of Conics - 4.4 Exercises - Page 349: 80

#### Answer

$\dfrac{x^2}{4}-\dfrac{(y-1)^2}{4/3}=1$

#### Work Step by Step

The standard form of the equation of the hyperbola with a horizontal transverse axis can be expressed as: $\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$ and 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: $\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1$ and vertices and foci have the form $(0, \pm, a)$ and $(0, \pm c)$. The center is the midpoint of the vertices : $(0,1)$ We have: $a=2$ $\dfrac{x^2}{4}-\dfrac{(y-2)^2}{b^2}=1$ or, $\dfrac{4^2}{4}-\dfrac{(3-1)^2}{b^2}=1$ $\implies b=\sqrt {\dfrac{4}{3}}$ Now, $\dfrac{x^2}{4}-\dfrac{(y-1)^2}{4/3}=1$

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