   Chapter 12.3, Problem 49E ### 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

# 37-50 Finding the equation of a Hyperbola Find an equation for the hyperbola that satisfies the given conditions.Foci ( ± 5 , 0 ) , length of transverse axis: 6

To determine

To find:

The equation for the hyperbola when the foci are (±5,0), and the length of the transverse axis is 6.

Explanation

Given:

The foci are (±5,0), and the length of the transverse axis is 6.

Approach:

The general equation of a hyperbola with x-axis as the transverse axis is given by,

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

b2=c2a2 ...(2)

l=2a ...(3)

Here, a is the transverse axis and b is the conjugate axis and c is the focus and (h,k) is the center of the hyperbola and l is the length of the transverse axis.

Calculation:

Since,

foci are (±5,0).

Use the midpoint formula to find h and k.

(h+c+hc2,k+k2)=(552,0+02)(h,k)=(0,0)

So, h=0, k=0

Since the length of the transverse axis is 6. Then,

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