Find the equation of the ellipse which has eccentricity = 1/2, distance between foci = 2 and a > b.

We need to find the equation of an ellipse of the form
x^2/a^2 + y^2/b^2 = 1 with eccentricity 1/2 and the distance between the foci equal to
2.

c = a*e = distance from center to either of the foci. c
= 1, e = (1/2)

=> 1 =
a*(1/2)

=> a = 2

b =
sqrt (a^2 - c^2)

=> sqrt ( 2^2 -
1^2)

=> sqrt
3

The equation of the ellipse is x^2/4 +
y^2/3 = 1