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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.

39. Foci: ( ± 4 , 0 ) , vertices: ( ± 5 , 0 ) .

To determine

The equation for the ellipse for the given conditions.

Explanation

Given:

The foci and vertices of the ellipse is,

Foci: (±4,0)

Vertices: (±5,0)

Approach:

The basic equation for an ellipse which is used is as follows,

x2a2+y2b2=1

Where a and b are constant values.

Expression to find vertices is,

V=(±a,0)

Expression to find Foci is,

F=(±c,0),

Where, c2=a2b2

Calculation:

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

V=(±a,0)=(±5,0)

Thus,

a=5.

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

F=(±c,0)=(±4,0)

Thus,

c=4.

Also as,

c2=a2b2

Substitute 4 for c and 5 for a in the above relation to calculate the value of b

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