# 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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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`