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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

Find an equation for the hyperbola with foci ( 0 , ± 5 ) and with asymptotes y = ± 3 4 x .

To determine

To find:

An equation for the hyperbola with foci (0,±5) and the asymptotes y=±34x.

Explanation

Given:

The foci and asymptotes of the hyperbola are (0,±5) and y=±34x.

Approach:

From asymptotes take the value of ab and use the relation c2=a2+b2… (1)

Calculation:

Since the foci (0,±5) of the hyperbola are lying on the y-axis. Foci are equidistance from the origin and c=5. So the hyperbola must be centered at the origin and has a vertical transverse axis.

Compare y=±34x with y=±abx, we can write ab=34.

From equation (1)

c2=a2+b2

c2b2=a2

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Chapter 12 Solutions

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Sect-12.1 P-11ESect-12.1 P-12ESect-12.1 P-13ESect-12.1 P-14ESect-12.1 P-15ESect-12.1 P-16ESect-12.1 P-17ESect-12.1 P-18ESect-12.1 P-19ESect-12.1 P-20ESect-12.1 P-21ESect-12.1 P-22ESect-12.1 P-23ESect-12.1 P-24ESect-12.1 P-25ESect-12.1 P-26ESect-12.1 P-27ESect-12.1 P-28ESect-12.1 P-29ESect-12.1 P-30ESect-12.1 P-31ESect-12.1 P-32ESect-12.1 P-33ESect-12.1 P-34ESect-12.1 P-35ESect-12.1 P-36ESect-12.1 P-37ESect-12.1 P-38ESect-12.1 P-39ESect-12.1 P-40ESect-12.1 P-41ESect-12.1 P-42ESect-12.1 P-43ESect-12.1 P-44ESect-12.1 P-45ESect-12.1 P-46ESect-12.1 P-47ESect-12.1 P-48ESect-12.1 P-49ESect-12.1 P-50ESect-12.1 P-51ESect-12.1 P-52ESect-12.1 P-53ESect-12.1 P-54ESect-12.1 P-55ESect-12.1 P-56ESect-12.1 P-57ESect-12.1 P-58ESect-12.1 P-59ESect-12.1 P-60ESect-12.1 P-61ESect-12.1 P-62ESect-12.1 P-63ESect-12.1 P-64ESect-12.1 P-65ESect-12.1 P-66ESect-12.2 P-1ESect-12.2 P-2ESect-12.2 P-3ESect-12.2 P-4ESect-12.2 P-5ESect-12.2 P-6ESect-12.2 P-7ESect-12.2 P-8ESect-12.2 P-9ESect-12.2 P-10ESect-12.2 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