# The foci of an ellipse are $$(\pm 2, 0)$$ and its eccentricity is 1/2, find its equation.

## Solution :

Let the equation of the ellipse be $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1.

Then, coordinates of the foci are $$(\pm ae, 0)$$.

Therefore,  ae = 2 $$\implies$$  a = 4

We have $$b^2$$ = $$a^2(1 – e^2)$$ $$\implies$$ $$b^2$$ =12

Thus, the equation of the ellipse is $$x^2\over 16$$ + $$y^2\over 12$$ = 1

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