高中一道圆锥曲线大题已知椭圆x^2/a^2+y^2/b^2=1(a>b>0)的离心率e=√3/3,MN是经过椭圆左焦点F的任一弦,AB是经过椭圆中心O且平行于MN的弦.(1)若2向量MF=5向量FN,求弦MN所在直线的斜率;(2)证
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![高中一道圆锥曲线大题已知椭圆x^2/a^2+y^2/b^2=1(a>b>0)的离心率e=√3/3,MN是经过椭圆左焦点F的任一弦,AB是经过椭圆中心O且平行于MN的弦.(1)若2向量MF=5向量FN,求弦MN所在直线的斜率;(2)证](/uploads/image/z/8489035-19-5.jpg?t=%E9%AB%98%E4%B8%AD%E4%B8%80%E9%81%93%E5%9C%86%E9%94%A5%E6%9B%B2%E7%BA%BF%E5%A4%A7%E9%A2%98%E5%B7%B2%E7%9F%A5%E6%A4%AD%E5%9C%86x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%28a%EF%BC%9Eb%EF%BC%9E0%29%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87e%3D%E2%88%9A3%2F3%2CMN%E6%98%AF%E7%BB%8F%E8%BF%87%E6%A4%AD%E5%9C%86%E5%B7%A6%E7%84%A6%E7%82%B9F%E7%9A%84%E4%BB%BB%E4%B8%80%E5%BC%A6%2CAB%E6%98%AF%E7%BB%8F%E8%BF%87%E6%A4%AD%E5%9C%86%E4%B8%AD%E5%BF%83O%E4%B8%94%E5%B9%B3%E8%A1%8C%E4%BA%8EMN%E7%9A%84%E5%BC%A6.%EF%BC%881%EF%BC%89%E8%8B%A52%E5%90%91%E9%87%8FMF%EF%BC%9D5%E5%90%91%E9%87%8FFN%2C%E6%B1%82%E5%BC%A6MN%E6%89%80%E5%9C%A8%E7%9B%B4%E7%BA%BF%E7%9A%84%E6%96%9C%E7%8E%87%EF%BC%9B%EF%BC%882%EF%BC%89%E8%AF%81)
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