   Chapter 12.CT, Problem 3CT ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Find the vertices, foci, and asymptotes of the hyperbola y 2 9 − x 2 16 + = 1 . Then sketch its graph

To determine

To find:

The vertices, foci and asymptotes of the hyperbola y29x216=1, and sketch the graph.

Explanation

Given:

The equation of the hyperbola is y29x216=1.

Approach:

Compare the given equation of hyperbola with y2a2x2b2=1.

Calculation:

By comparing the given equation of up-down hyperbola y29x216=1 with y2a2x2b2=1.

Since a2=9 and b2=16, so a=3 and b=4 and c=±a2b2=±9+16=±5. The vertices are 3 units up and down to the center (0,0) and the foci are 5 units up and down to the center (0,0)

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