已知椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)的离心率为√6/3,短轴的一个端点到右焦点的距离为√3..设直线L与椭圆C交于A,B两点,坐标原点O到直线的距离为√3/2,求三角形AOB的面积的最大值
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![已知椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)的离心率为√6/3,短轴的一个端点到右焦点的距离为√3..设直线L与椭圆C交于A,B两点,坐标原点O到直线的距离为√3/2,求三角形AOB的面积的最大值](/uploads/image/z/6858097-25-7.jpg?t=%E5%B7%B2%E7%9F%A5%E6%A4%AD%E5%9C%86C%EF%BC%9Ax%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%28a%3Eb%3E0%29%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%E4%B8%BA%E2%88%9A6%2F3%2C%E7%9F%AD%E8%BD%B4%E7%9A%84%E4%B8%80%E4%B8%AA%E7%AB%AF%E7%82%B9%E5%88%B0%E5%8F%B3%E7%84%A6%E7%82%B9%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA%E2%88%9A3..%E8%AE%BE%E7%9B%B4%E7%BA%BFL%E4%B8%8E%E6%A4%AD%E5%9C%86C%E4%BA%A4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9O%E5%88%B0%E7%9B%B4%E7%BA%BF%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA%E2%88%9A3%2F2%2C%E6%B1%82%E4%B8%89%E8%A7%92%E5%BD%A2AOB%E7%9A%84%E9%9D%A2%E7%A7%AF%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC)
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