   Chapter 12.CR, Problem 60E ### 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

# 55–64 ■ Finding the Equation of a Conic Find an equation for the conic section with the given properties.The hyperbola with center C ( 2 , 4 ) , foci F 1 ( 2 , 1 ) and F 2 ( 2 , 7 ) , and vertices V 1 ( 2 , 6 ) and V 2 ( 2 , 2 ) .

To determine

To find:

The equation for the conic section.

Explanation

Given:

The hyperbola with center C(2,4), foci F1(2,1) and F2(2,7), and vertices V1(2,6) and V2(2,2).

Approach:

The distance between the vertices is 2a.

The distance between the foci is 2c.

c2=a2+b2(1)

The equation of hyperbola with vertical transverse axis is given by:

(yk)2a2(xh)2b2=1.

Calculation:

Center is C(2,4), thus h=2, k=4.

The distance between V1(2,6) and V2(2,2) is 62=4, so a=2

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