椭圆x^2/6+y^2/2=1
右焦点（2,0)
园N:x^2+(y-2)^2=1由圆的参数方程设
点E(2+cosα.sinα) ,F(2-cosα,-sinα)
P(x,y),y^2=2-x^2/3,x∈ [-√6,√6]
u=向量PE点乘向量PF
=(2+cosα-x,sinα-y)*(2-cosα-x,-sinα-y)
=(2+cosα-x)(2-cosα-x)+(sinα-y)(-sinα-y)
= (2-x)^2-cos²ā+y^2-sin²α
= (2-x)^2+y^2-1
= x^2-4x+5-x^2/3=2/3 *x^2 -4x +5
=2/3(x-3)^2-1
∴x=3,u取 最小值-1
x=-√6 u取 最大值9+4√6
向量PE点乘向量PF的最大值是9+4√6