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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