   Chapter 12.2, Problem 48E ### 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

# 39-56 Finding the Equation of an Ellipse Find an equation for the ellipse that satisfies the given conditions.48. Foci: ( ± 5 , 0 ) , length of major axis: 12 .

To determine

The equation for the ellipse for the given conditions.

Explanation

Given:

The foci and length of minor axis of the ellipse are,

Foci: (±5,0),

Length of major axis: 12.

Approach:

The basic equation for an ellipse with a horizontal major axis which is used is as follows,

x2a2+y2b2=1

Where a and b are constant values.

Formula to find major axis,

MajorAxis=2a

Expression to find Foci is,

F=(±c,0),

Where, c2=a2b2

Calculation:

Compare the standard formula for length of the major axis and the given length of the major axis.

MajorAxis=2a=12

Thus,

2a=12a=122a=6.

Compare the standard coordinates of foci and the given coordinates of foci.

F=(±c,0)=(±5,0)

Thus,

c=5

Also as,

c2=a2b2

Substitute 5 for c and 6 for a in the formula to calculate the value of b

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