已知椭圆x²/a²+y平方/b平方=1(a>b>0)的离心率是(根号6)/3,F是其左焦点,若直线x-(根号6)y=0与椭圆交于A、B两点,且向量FA·向量FB=-1,求该椭圆的方程.
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![已知椭圆x²/a²+y平方/b平方=1(a>b>0)的离心率是(根号6)/3,F是其左焦点,若直线x-(根号6)y=0与椭圆交于A、B两点,且向量FA·向量FB=-1,求该椭圆的方程.](/uploads/image/z/6855661-37-1.jpg?t=%E5%B7%B2%E7%9F%A5%E6%A4%AD%E5%9C%86x%26%23178%3B%2Fa%26%23178%3B%2By%E5%B9%B3%E6%96%B9%2Fb%E5%B9%B3%E6%96%B9%3D1%28a%EF%BC%9Eb%EF%BC%9E0%29%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%E6%98%AF%28%E6%A0%B9%E5%8F%B76%29%2F3%2CF%E6%98%AF%E5%85%B6%E5%B7%A6%E7%84%A6%E7%82%B9%2C%E8%8B%A5%E7%9B%B4%E7%BA%BFx-%28%E6%A0%B9%E5%8F%B76%29y%3D0%E4%B8%8E%E6%A4%AD%E5%9C%86%E4%BA%A4%E4%BA%8EA%E3%80%81B%E4%B8%A4%E7%82%B9%2C%E4%B8%94%E5%90%91%E9%87%8FFA%C2%B7%E5%90%91%E9%87%8FFB%3D-1%2C%E6%B1%82%E8%AF%A5%E6%A4%AD%E5%9C%86%E7%9A%84%E6%96%B9%E7%A8%8B.)
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