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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

SKILLS

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

Eccentricity: 1 3 , foci: ( 0 , ± 2 )

To determine

The equation for the ellipse for the given conditions.

Explanation

Approach:

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

x2b2+y2a2=1(1)

Here, a and b are constant values.

The formula to calculate the eccentricity in the number is given as,

e=ca(2)

Here, c is a2b2 and the eccentricity of every ellipse satisfies 0<e<1.

The expression to find the foci is given as,

F=(±c,0)

Given:

The eccentricity is 13 and the foci are (0,±2) of an ellipse.

Calculation:

Since the foci is (0,±2), then the value of c will be 2.

Calculate the value of major length.

Substitute 13 for e and 2 for c in equation (2) to calculate the major length.

13=2aa=213=6

Calculate the value of minor length

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