依题意,椭圆方程是x^2/4+y^2/3=1,

　　左右顶点为A1(-2,0),A2(2,0）,右焦点F2为(1,0),

　　设椭圆上的动点P为(2cost,√3sint),

　　则A1P的斜率=√3sint/[2cost+2]=√3sint/[2(cost+1)],

　　A1P:y=(x+2)√3sint/[2(cost+1)]交直线x=4于M(4,6√3sint/[2(cost+1)]),

　　同理A2P:y=(x-2)√3sint/[2(cost-1)]交直线x=4于M(4,2√3sint/[2(cost-1)]),

　　∴向量F2M*F2N=(3,6√3sint/[2(cost+1)])*(3,2√3sint/[2(cost-1)])

　　=9+6√3sint/[2(cost+1)]*2√3sint/[2(cost-1)]

　　=9+9(sint)^2/[(cost)^2-1]

　　=0,

　　∴点F2在以MN为直径的圆上.

　　=