设椭圆E的中心在坐标原点O,焦点在x轴上,短轴长为4,点M(2,√2)在椭圆上,设动直线L交椭圆E于A,B两点,且OA⊥OB,求△OAB的面积的取值范围(已算出AB始终与x^2+y^2=8/3相切,最好能接着做下去,给出
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![设椭圆E的中心在坐标原点O,焦点在x轴上,短轴长为4,点M(2,√2)在椭圆上,设动直线L交椭圆E于A,B两点,且OA⊥OB,求△OAB的面积的取值范围(已算出AB始终与x^2+y^2=8/3相切,最好能接着做下去,给出](/uploads/image/z/8035382-38-2.jpg?t=%E8%AE%BE%E6%A4%AD%E5%9C%86E%E7%9A%84%E4%B8%AD%E5%BF%83%E5%9C%A8%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9O%2C%E7%84%A6%E7%82%B9%E5%9C%A8x%E8%BD%B4%E4%B8%8A%2C%E7%9F%AD%E8%BD%B4%E9%95%BF%E4%B8%BA4%2C%E7%82%B9M%EF%BC%882%2C%E2%88%9A2%EF%BC%89%E5%9C%A8%E6%A4%AD%E5%9C%86%E4%B8%8A%2C%E8%AE%BE%E5%8A%A8%E7%9B%B4%E7%BA%BFL%E4%BA%A4%E6%A4%AD%E5%9C%86E%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E4%B8%94OA%E2%8A%A5OB%2C%E6%B1%82%E2%96%B3OAB%E7%9A%84%E9%9D%A2%E7%A7%AF%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%EF%BC%88%E5%B7%B2%E7%AE%97%E5%87%BAAB%E5%A7%8B%E7%BB%88%E4%B8%8Ex%5E2%2By%5E2%3D8%2F3%E7%9B%B8%E5%88%87%2C%E6%9C%80%E5%A5%BD%E8%83%BD%E6%8E%A5%E7%9D%80%E5%81%9A%E4%B8%8B%E5%8E%BB%2C%E7%BB%99%E5%87%BA)
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