   Chapter 12.3, Problem 3E ### 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

# CONCEPTSThe graph of the equation y 2 a 2 − x 2 b 2 = 1 with a > 0 , b > 0 is a hyperbola with the ________ (horizontal/vertical) transverse axis, vertices ( ________ , ________ ) and ( ________ , ________ ) and foci ( ± c , 0 ) , where c = ________ . So the graph of y 2 4 2 − x 2 3 2 = 1 is a hyperbola with vertices ( ________ , ________ ) and ( ________ , ________ ) and foci ( ________ , ________ ) and ( ________ , ________ ).

To determine

To fill:

Explanation

Given:

The graph of the equation y2a2x2b2=1 with a>0,b>0 is a hyperbola with the ______ (horizontal/vertical) transverse axis, vertices (______, ______) and (______, ______) and foci (0,±c), where c=______. So the graph of y242x232=1 is a hyperbola with vertices (______, ______) and (______, ______) and foci (______, ______) and (______, ______).

Approach:

Based on the basic definition of a hyperbola, for the equation y2a2x2b2=1, the y-intercepts are ±a and b2=c2a2, where (0,±c) are the foci.

Therefore, the graph of the equation y2a2x2b2=1 with a>0,b>0 is a hyperbola with the horizontal transverse axis, vertices (0,a) and (0,a) and foci (0,±c), where c=a2+b2

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