椭圆x^2/9+y^2/25=1上一点M到焦点F1的距离是3,N是MF1的中点,则△MOF1的周长为

c=±√(25-9)=±4,F1(0,-4),F2(0,4).|F1F2|=8.a=3,b=5.|MF1|=3.
|MF1|+|MF2|=2b=2*5=10.
|MF2|=10-|MF1|=10-3=7.
设M点的坐标为M(x1,y1),则：
y1^2=|MF1|-[x-(-4)]^2=|MF2|^2-(4-x)^2.
3^2-(x+4)^2=7^2-(4-x)^2.
9-x^2-8x-16=49-x^2+8x-16.
-16x=40.
x=-5/2
y^2=3^2-(-5/2+4)^2.
y^2=27/4.
Y=3√3/2.
|MO|=√(-5/2)^2+(27/4).
=√13.
∴△MOF1的周长L={MF1|+|F1O|+MO|=3+|-4|+√13.
即,L=7+√13.（长度单位）.-----即为所求.