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Determine the equation of an ellipse if the centre of the ellipse is at the origin and...

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lilian-0716 | Student | Salutatorian

Posted October 6, 2013 at 6:59 AM via web

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Determine the equation of an ellipse if the centre of the ellipse is at the origin and foci are(+-8,0) , vertices (0,+-8)

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aruv | High School Teacher | Valedictorian

Posted October 6, 2013 at 7:18 AM (Answer #1)

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Centre =(0,0)

Foci= `(+-8,0)`

Vertices =`(0,+-8)`

Let foci of the ellipse be `(+-ae,0)`

Thus

ae=8     (i)

But  we know `b^2=a^2(1-e^2)`, where b and a are respectively semi minor and major axis.

Thus

`64=a^2-a^2e^2=a^2-64`

`128=a^2`  

So required equation of the ellipse is

`x^2/128+y^2/64=1`

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