已知椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)的离心率为1/2,以原点为圆心,椭圆的短半轴为半径的圆与x-y+sqrt(6)=0相切.(1)求椭圆C的方程;(2)设过点P(4,0)的直线l与椭圆相交于A,B两点,E是B关于x轴的对称点.
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![已知椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)的离心率为1/2,以原点为圆心,椭圆的短半轴为半径的圆与x-y+sqrt(6)=0相切.(1)求椭圆C的方程;(2)设过点P(4,0)的直线l与椭圆相交于A,B两点,E是B关于x轴的对称点.](/uploads/image/z/3700354-58-4.jpg?t=%E5%B7%B2%E7%9F%A5%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%BA1%2F2%2C%E4%BB%A5%E5%8E%9F%E7%82%B9%E4%B8%BA%E5%9C%86%E5%BF%83%2C%E6%A4%AD%E5%9C%86%E7%9A%84%E7%9F%AD%E5%8D%8A%E8%BD%B4%E4%B8%BA%E5%8D%8A%E5%BE%84%E7%9A%84%E5%9C%86%E4%B8%8Ex-y%2Bsqrt%286%29%3D0%E7%9B%B8%E5%88%87.%EF%BC%881%EF%BC%89%E6%B1%82%E6%A4%AD%E5%9C%86C%E7%9A%84%E6%96%B9%E7%A8%8B%EF%BC%9B%EF%BC%882%EF%BC%89%E8%AE%BE%E8%BF%87%E7%82%B9P%284%2C0%29%E7%9A%84%E7%9B%B4%E7%BA%BFl%E4%B8%8E%E6%A4%AD%E5%9C%86%E7%9B%B8%E4%BA%A4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2CE%E6%98%AFB%E5%85%B3%E4%BA%8Ex%E8%BD%B4%E7%9A%84%E5%AF%B9%E7%A7%B0%E7%82%B9.)
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