椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)的离心率为√3/3,过右焦点F的直线L与C相交于A、B两点,当l的斜率为1时坐标原点O到L的距离为√2/2.(1)求a,b的值(2)C上是否存在点P,使得当L绕F转到某一位置时,有向量
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![椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)的离心率为√3/3,过右焦点F的直线L与C相交于A、B两点,当l的斜率为1时坐标原点O到L的距离为√2/2.(1)求a,b的值(2)C上是否存在点P,使得当L绕F转到某一位置时,有向量](/uploads/image/z/5925958-70-8.jpg?t=%E6%A4%AD%E5%9C%86C%3Ax%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%9A3%2F3%2C%E8%BF%87%E5%8F%B3%E7%84%A6%E7%82%B9F%E7%9A%84%E7%9B%B4%E7%BA%BFL%E4%B8%8EC%E7%9B%B8%E4%BA%A4%E4%BA%8EA%E3%80%81B%E4%B8%A4%E7%82%B9%2C%E5%BD%93l%E7%9A%84%E6%96%9C%E7%8E%87%E4%B8%BA1%E6%97%B6%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9O%E5%88%B0L%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA%E2%88%9A2%2F2.%EF%BC%881%EF%BC%89%E6%B1%82a%2Cb%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89C%E4%B8%8A%E6%98%AF%E5%90%A6%E5%AD%98%E5%9C%A8%E7%82%B9P%2C%E4%BD%BF%E5%BE%97%E5%BD%93L%E7%BB%95F%E8%BD%AC%E5%88%B0%E6%9F%90%E4%B8%80%E4%BD%8D%E7%BD%AE%E6%97%B6%2C%E6%9C%89%E5%90%91%E9%87%8F)
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