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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.

49. Endpoints of major axis: ( ± 10 , 0 ) , distance between foci: 6 .

To determine

The equation for the ellipse for the given conditions.

Explanation

Given:

Endpoints of major axis: (±10,0).

Distance between foci: 6.

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.

Expression of end points of major principal axis is,

MajorAxis=(±a,0)

Expression to find the distance of Foci is,

F=2c,

Where, c2=a2b2

Calculation:

Compare the standard coordinates of end points of the major axis and the given coordinate of major axis.

MajorAxis=(±a,0)=(±10,0)

Thus,

a=10.

Compare the standard notation of the distance of foci and the given the distance of foci.

F=2c=6

Thus,

2c=6c=62c=3

Also as,

c2=a2b2

Substitute 3 for c and 10 for a in the formula to calculate the value of b

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