Dear friends,
   My name is Helen. I'm 12 years old. I  1  from Taxas, America. I’m really  2   in Chinese geography. It's fun! And I hope you can tell me more. I like hamburgers best,  3   I try to eat them twice a week  4   it's a kind of   5   food. And I like to drink lemon  6   . As for sports, I often go swimming with my parents on weekends.
   I   7  in Cobb Street School. My   8  subjects in school are ME and art. They are really fun! After school, I like to go to the   9   with my family or friends. I like action movies and cartoons. They’re  10   How about you? Do you often go to the cinema with your family or friends?
                                                                                                                                                                   Yours,
                                                                                                                                                                   Helen

数一数，填一填，答一答。

已知椭圆C：$\frac{x^2}{a^2}+\frac{y^2}{b^2}$=1（a＞b＞0）的右焦点为F（1，0），短轴的一个端点B到F的距离等于焦距．

（Ⅰ）求椭圆C的方程；

（Ⅱ）过点F的直线l与椭圆C交于不同的两点M，N，是否存在直线l，使得△BFM与△BFN的面积比值为2？若存在，求出直线l的方程；若不存在，说明理由．