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已知点A(x 1 ,y 1 ),B(x 2 ,y 2 )(x 1 x 2 ≠0)是抛物线y 2 =2px(p>0)上的两个动点,O是坐标原点,向量 满足 ,C的方程为x 2 +y 2 -(x 1 +x 2 )x-(y 1 +y 2 )y=0。 (1)证明线段AB是圆C的直径; (2)当圆C的圆心到直线x-2y=0的距离的最小值为 时,求p的值。
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