(1) 设P(x,y)
向量NM=(-2,0)
向量NP=(x-1,y)
向量PM=(-1-x,-y)
向量NM·NP=2-2x
PM·PN=x^2+y^2-1
MP·MN=2+2x
成公差为非负的等差数列
2=x^2+y^2-1
x^2+y^2=3
(2)
cosa=向量PM*向量PN/(|向量PM|*|向量PN|)
=(x^2+y^2-1)/[√(x^2-2x+1+y^2)*√(x^2+2x+1+y^2)]
=2/[√(4-2x)*√(4+2x)]
=2/√(16-4x^2)
x^2=0 cosa 最小值=1/2
a=60°
x=0]
P(0,±√3)