Would you date someone who has a history of eating disorders?

Would you date someone who has a history of eating disorders?
i used to be anorexic, but am better now. I'm 22 and when I was 15 when I was sick. People still think I have eating troubles however, because I'm still pretty slim, and watch what I eat. I'v also know that some people think I'm bulimic, however I'm not.

Would you date someone who

A)has a rumour about them being bulimic

b) date someone who used to have an eating disorder but is now better