设A(x1,y1),B(x2,y2),P（0,m）
向量AP=向量3PB
(-x1,m-y1)=3(x2,y2-m),x1=-3x2
Y=kx+m 与椭圆2x^2+y^2=1联立整理得
(k^2+2)x^2+2kmx+m^2-1=0
X1+x2=-2x2=-2km/(k^2+2),
x2=km/(k^2+2) (1)
X1*x2=( m^2-1)/(k^2+2)=-3x2^2,(2)
将(1)代入(2)
-3[km/(k^2+2)]^2=( m^2-1)/(k^2+2),
整理得k^2=(2-2m^2)/(4m^2-1)
Delt=(2kmx)^2-4(k^2+2)(m^2-1)>0,
整理得k^2-2m^2+2>0
将k^2=(2-2m^2)/(4m^2-1)代入,整理得m^2(m^2-1)/(4m^2-1)