(1)设动点的坐标为P(x,y),则=(x,y-1),=(x,y+1),=(1-x,-y) ∵·=k||2,∴x2+y2-1=k[(x-1)2+y2] 即(1-k)x2+(1-k)y2+2kx-k-1=0. 若k=1,则方程为x=1,表示过点(1,0)是平行于y轴的直线. 若k≠1,则方程化为:,表示以(-,0)为圆心,以为半径的圆. (2)当k=2时,方程化为(x-2)2+y2=1.∵2+=2(x,y-1)+(x,y+1)=(3x,3y-1), ∴|2+|=.又x2+y2=4x-3,∴|2+|= ∵(x-2)2+y2=1,∴令x=2+cosθ,y=sinθ, 则36x-6y-26=36cosθ-6sinθ+46=6cos(θ+φ)+46∈[46-6,46+6], ∴|2+|max==3+,|2+|min==-3. |