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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

39-56 Finding the Equation of an Ellipse Find an equation for the ellipse that satisfies the given conditions.

47. Foci: ( 0 , ± 2 ) , length of minor axis: 6 .

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: (0,±2),

Length of minor axis: 6.

Approach:

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

x2b2+y2a2=1

Where a and b are constant values.

Formula to find minor axis,

MinorAxis=2b

Expression to find Foci is,

F=(0,±c),

Where, c2=a2b2

Calculation:

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

MinorAxis=2b=6

Thus,

2b=6b=62b=3.

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

F=(0,±c)=(0,±2)

Thus,

c=2

Also as,

c2=a2b2

Substitute 2 for c and 3 for b in the formula to calculate the value of a

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