Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 13 - Cumulative Review - Page 970: 53

Answer

The graph is a hyperbola which opens up and down with center point at $(0,0)$ and vertices at points $(0,3)$ and $(0-3)$.

Work Step by Step

The graph of an equation of the form $$\frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}} =1$$ is a hyperbola with center point at $(0,0)$ and y-intercepts $(0,a)$ and $(0,-a)$. Hence, the equation $$4(y^2)-9(x^2)=36$$ may be rewritten to $$\frac{y^{2}}{9}-\frac{x^{2}}{4} =1$$ by dividing both sides by $\frac{1}{36}$. Now, the center is at (0,0). Since $y$ is positive, we know that the hyperbola will open up and down with vertices equal to $$a^{2} = 9$$ $$\sqrt{a^{2}}=9$$ $$a=±3$$ or points $(0,3)$ and $(0-3)$.
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