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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

CONCEPTS

The graph of the equation x 2 a 2 y 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 x 2 4 2 y 2 3 2 = 1 is a hyperbola with vertices ( ________ , ________ ) and ( ________ , ________ ) and foci ( ________ , ________ ) and ( ________ , ________ ).

To determine

To fill:

The blanks with appropriate answers.

Explanation

Given:

The graph of the equation x2a2y2b2=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 x242y232=1 is a hyperbola with vertices (______, ______) and (______, ______) and foci (______, ______) and (______, ______).

Approach:

Based on the basic definition of a hyperbola, for the equation x2a2y2b2=1, the x-intercepts are ±a and b2=c2a2, where (±c,0) are the foci.

Therefore, the graph of the equation x2a2y2b2=1 with a>0,b>0 is a hyperbola with the horizontal transverse axis, vertices (a,0) and (a,0) and foci (±c,0), where c=a2+b2

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Chapter 12 Solutions

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