如图,F1,F2是椭圆x^2/a^2+y^2/b^2=1的左右焦点,点M在x轴上,且向量OM=√3/2向量OF2,过点F2的直线与椭圆交与A,B两点,且AM垂直于X轴,向量AF1*向量AF2=0(1)求椭圆的离心率(2)若三角形ABF1的周长为4√6,
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![如图,F1,F2是椭圆x^2/a^2+y^2/b^2=1的左右焦点,点M在x轴上,且向量OM=√3/2向量OF2,过点F2的直线与椭圆交与A,B两点,且AM垂直于X轴,向量AF1*向量AF2=0(1)求椭圆的离心率(2)若三角形ABF1的周长为4√6,](/uploads/image/z/1592399-47-9.jpg?t=%E5%A6%82%E5%9B%BE%2CF1%2CF2%E6%98%AF%E6%A4%AD%E5%9C%86x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%E7%9A%84%E5%B7%A6%E5%8F%B3%E7%84%A6%E7%82%B9%2C%E7%82%B9M%E5%9C%A8x%E8%BD%B4%E4%B8%8A%2C%E4%B8%94%E5%90%91%E9%87%8FOM%3D%E2%88%9A3%2F2%E5%90%91%E9%87%8FOF2%2C%E8%BF%87%E7%82%B9F2%E7%9A%84%E7%9B%B4%E7%BA%BF%E4%B8%8E%E6%A4%AD%E5%9C%86%E4%BA%A4%E4%B8%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E4%B8%94AM%E5%9E%82%E7%9B%B4%E4%BA%8EX%E8%BD%B4%2C%E5%90%91%E9%87%8FAF1%2A%E5%90%91%E9%87%8FAF2%3D0%EF%BC%881%EF%BC%89%E6%B1%82%E6%A4%AD%E5%9C%86%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%EF%BC%882%EF%BC%89%E8%8B%A5%E4%B8%89%E8%A7%92%E5%BD%A2ABF1%E7%9A%84%E5%91%A8%E9%95%BF%E4%B8%BA4%E2%88%9A6%2C)
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