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设点M(x,y)到直线x=4的距离与它到定点(1,0)的距离之比为2,并记点M的轨迹曲线为C, (Ⅰ)求曲线C的方程; (Ⅱ)设过定点(0,2)的直线l与曲线C交于不同的两点E,F,且∠EOF=90°(其中O为坐标原点),求直线l的斜率k的值; (Ⅲ)设A(2,0),B(0, )是曲线C的两个顶点,直线y=mx(m>0)与线段AB相交于点D,与椭圆相交于E,F两点,求四边形AEBF面积的最大值。
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