   Chapter 12.CT, Problem 13CT ### 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

# Find an equation for the ellipse with center ( 2 , 0 ) , foci ( 2 , ± 3 ) and major axis of length 8 .

To determine

To find:

An equation for the ellipse with center (2,0), foci (2,±3) and major axis of length 8.

Explanation

Given:

The center and foci of the ellipse are (2,0) and (2,±3); and length of the major axis is 8 unit.

Approach:

The length of the major axis is given, so use it to find a and since foci are c units away from the center. Then by the relation c2=a2b2, the value b can be calculated. The equation of the vertically shifted ellipse is (xh)2a2+(yk)2b2=1.

Calculation:

The length of the major axis is 2a=8 units, so a=4. The foci are 3 units up and down to the center, so c=3.

Since b=a2c2 so b=169=7.

Center of the ellipse is (h,k)=(2,0), It means h=2 and k=0

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