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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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

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