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Let the maximum area of the triangle that can be inscribed in the ellipse x^2 \over a^2 + y^2 \over 4 = 1,\,a > 2, having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be 6√ 3 . Then the eccentricity of the ellipse is : | Watch the step-by-step video solution for this NIMCET PYQ.