Let the maximum area of the triangle that can be inscribed in the ellipse \( \frac{x^{2}}{a^{2}}...

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Let the maximum area of the triangle that can be inscribed in the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{4}=1, a2 \), 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 \( 6 \sqrt{3} \). Then the exxentricity of the ellispe is:
(a) \( \frac{\sqrt{3}}{2} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{1}{\sqrt{2}} \)
(d) \( \frac{\sqrt{3}}{4} \)
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