Answer
$y=-\frac{4}{9}x$ and $y=\frac{4}{9}x$
Work Step by Step
Based on the given hyperbola, the transverse axis is vertical with center $(0,0)$, thus we have asymptotes
$y=\pm \frac{b}{a}x=\pm\frac{\sqrt {16}}{\sqrt {81}}x=\pm\frac{4}{9}x$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 9 - Analytic Geometry - Section 9.4 The Hyperbola - 9.4 Assess Your Understanding - Page 689: 14
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