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(1)e=(根2)/2, a^2=2c^2=b^2+c^2所以b=c=a*(根2)/2M(0,b),F(b,0),B(b*根2,0)向量MF(b,-b),FB(b*(根2-1),0)MF*MB=(根2-1)*b^2=根2-1b=1a=根2x^2/2+y^2=1(2)F为垂心,所以MF垂直于PQ.MF斜率为-1,所以PQ斜率为1设PQ方程为:y=x+n,P(x1,y1);Q(x2,y2)代入椭圆得:3x^2+4nx+2n^2-2=0x1+x2=-4n/3,x1x2=(2n^2-2)/3向量QF(1-x2,-y2),向量MP(x1,y1-1)QF*MP=x1-x1x2-y1y2+y2=x1-x1x... |
