设点F1(-c,0),F2(c,0)分别是椭圆C:x^2/a^2+y^2=1(a>1)的左,右焦点,P为椭圆C上任意一点

令P点(x,y)
则：x=acost,y=sint
PF1=(-c,0)-(x,y)=(-c-x,-y)
PF2=(c,0)-(x,y)=(c-x,-y)
故：PF1·PF2=(-c-x,-y)·(c-x,-y)
=x^2+y^2-c^2=a^2cost^2+sint^2-c^2
=a^2(1+cos(2t))/2+(1-cos(2t))/2-c^2
=(a^2/2+1/2-c^2)+(a^2/2-1/2)cos(2t)
最小值：(a^2/2+1/2-c^2)-(a^2/2-1/2)
=1-c^2=0,故：c=1
即：a^2=b^2+c^2=2
故椭圆方程：x^2/2+y^2=1