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How do you find the eccentricity of an ellipse? equation: 44x^2+y^2=44

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pink88 | eNotes Newbie

Posted July 1, 2013 at 9:50 PM via web

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How do you find the eccentricity of an ellipse?

equation: 44x^2+y^2=44

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lfryerda | High School Teacher | (Level 2) Educator

Posted July 1, 2013 at 11:05 PM (Answer #1)

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Given an ellipse in the form `(x/a)^2+(y/b)^2=1` , its eccentricity is given by the formula `e=sqrt{1-(a/b)^2}`  when `b>a` .

This means that we need to divide both sides of the ellipse by 44 to get

`x^2+y^2/44=1`   

matching up the constants `a` and `b` , we see that `a=1` and `b^2=44` .

This means that the eccentricity is

`e=sqrt{1-a^2/b^2}`    sub in values

`=sqrt{1-1/44}`  simplify

`=sqrt{43/44}`

The eccentricity of the ellipse is `sqrt{43/44}` .

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