Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 10 - Analytic Geometry - 10.4 The Hyperbola - 10.4 Assess Your Understanding - Page 669: 18



Work Step by Step

The given hyperbola has the $y$-axis as the transverse axis; therefore we eliminate $(A)$ and $(B)$. We have to decide between $(C)$ and $(D)$. The vertices for the given hyperbola are: $(0,-1),(0,1)$ Check $(0,1)$ in equation $(C)$: $\dfrac{1^2}{4}-0^2\stackrel{?}{=}1$ $\dfrac{1}{4}\not=1$ So equation $(C)$ doesn't fit. Check $(0,1)$ in equation $(D)$: $1^2-\dfrac{0^2}{4}\stackrel{?}{=}1$ $1=1\checkmark$ So equation $(D)$ fits. Therefore, the correct answer is equation $(D)$.
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