椭圆X2/36+Y2/9=1上有俩动点PQ,E(3,0),EP垂直于EQ,则向量EP点乘向量QP的最小值为多少?答案是6
问题描述:
椭圆X2/36+Y2/9=1上有俩动点PQ,E(3,0),EP垂直于EQ,则向量EP点乘向量QP的最小值为多少?答案是6
答
E': x^2/36 + y^2/9 =1P,Q is on E'E(3,0)EP 垂直于EQlet P (x1,y1), Q(x2,y2)EP 垂直于EQ=>EP.EQ=0(x1-3,y1).(x2-3,y2)=0(x1-3)(x2-3)+ y1y2=0x1x2-3(x1+x2)+9 + y1y2=0EP.QP(x1-3,y1).(x1-x2,y1-y2)=(x1-3)(x1-x2)...