当且仅当k?0,即x1??x2,即???1时,Smin?分
1. ??????5622 （2）由题知A(x1,x1),B(x2,x2),且x1?x2,则直线AB的斜率
kAB2y2?y1x12?x2???x1?x2.x2?x1x2?x1设直线AB的方程为y?x12?k(x?x1),即y?(x1?x2)x?x1x2,则直线AB与抛物线C所围的面积S??[(x1?x2)x?x1x2?x2]dxx1x2
x1?x2112?x2?x1x2x?x3)|x?(x2?x1)3,x12364143因为S?,所以(x2?x1)?,得x2?x1?2. ??????8
363?(分
设M(x,y),则x?x1?x2?x1?1,22y1?y2x12?x2y???x12?2x1?2?(x1?1)2?1,
22所以y?x2?1.故点M的轨迹方程为y?x2?1.????10分
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