# pre-calculus

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the foci of an ellipse are (0,2) (0,-2) and the eccentricity is 1/2. determine the equation of the ellipse. write your answer in standard form.

• pre-calculus -

e = c/a = 1/2, so a = 2c
a^2 = c^2+b^2
4c^2 = c^2+b^2
3c^2 = b^2
c = 2, so b^2 = 12, and a^2 = 16

x^2/16 + y^2/12 = 1

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