设椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)的左、右焦点分别为F1、F2,上顶点为A,在X轴负半轴上有一点B,满足|BF1|=|F1F2|,且AB⊥AF2(1)求椭圆C的离心率;(2)若过A、B、F2三点的原恰好与直线l:x-√3y-3=0相切,求
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![设椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)的左、右焦点分别为F1、F2,上顶点为A,在X轴负半轴上有一点B,满足|BF1|=|F1F2|,且AB⊥AF2(1)求椭圆C的离心率;(2)若过A、B、F2三点的原恰好与直线l:x-√3y-3=0相切,求](/uploads/image/z/5184513-9-3.jpg?t=%E8%AE%BE%E6%A4%AD%E5%9C%86C%3Ax%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%28a%3Eb%3E0%29%E7%9A%84%E5%B7%A6%E3%80%81%E5%8F%B3%E7%84%A6%E7%82%B9%E5%88%86%E5%88%AB%E4%B8%BAF1%E3%80%81F2%2C%E4%B8%8A%E9%A1%B6%E7%82%B9%E4%B8%BAA%2C%E5%9C%A8X%E8%BD%B4%E8%B4%9F%E5%8D%8A%E8%BD%B4%E4%B8%8A%E6%9C%89%E4%B8%80%E7%82%B9B%2C%E6%BB%A1%E8%B6%B3%7CBF1%7C%3D%7CF1F2%7C%2C%E4%B8%94AB%E2%8A%A5AF2%EF%BC%881%EF%BC%89%E6%B1%82%E6%A4%AD%E5%9C%86C%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%EF%BC%9B%EF%BC%882%EF%BC%89%E8%8B%A5%E8%BF%87A%E3%80%81B%E3%80%81F2%E4%B8%89%E7%82%B9%E7%9A%84%E5%8E%9F%E6%81%B0%E5%A5%BD%E4%B8%8E%E7%9B%B4%E7%BA%BFl%3Ax-%E2%88%9A3y-3%3D0%E7%9B%B8%E5%88%87%2C%E6%B1%82)
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