Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Skill Practice - Page 645: 18

Answer

See below

Work Step by Step

The foci and vertices lie on the x-axis equidistant from the origin, so the transverse axis is vertical and the center is the origin. The foci are each 4 units from the center, so $c =4$. The vertices are each 2 units from the center, so $a=2 $. Find $b^2=c^2-a^2=4^2-2^2=12$ $b=\sqrt 12$ Because the transverse axis is vertical, the standard form of the equation is as follows: $$\frac{y^2}{4}-\frac{x^2}{12}=1$$
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