Hi there
I went through a period of not eating anywhere near enough and dropped massive amounts of weight. I didn't identify as anorexic as such, but I didn't deny I was slim and needed to eat more. However I didn't realise until later exactly how thin I had become and could see why people were worried and commenting. I was eating very little due to stress, so I'm happy now to admit is was obviously an eating disorder and under eating or not eating comes in various guises.
OP I hope you don't mind me joining in here, our experiences sound different, both the causes and the solutions, so maybe there are ideas to help in several stories.
I never went to therapy and didn't need to, as soon as I realised my Dad was as worried as he was, I started to eat more in front of him. I also never claimed to eat more than I did or not be underweight. I didn't get hungry but I was eating, really not enough, absolute minimum fruit and yogurt to get by. I would get faint and sometimes pass out. Once I saw this and some photographs of myself, plus several people voicing concerns, I started eating more and slowly gained the weight. I wouldn't every have it happen again, I've been vigilant ever since, to the point where I don't need to be any more. So it is possible for it to go and not be a concern anymore, with some time and care.
Vigilance at first by the person is important, if negative thought patterns or unhealthy eating habits are coming back.
I think identifying the cause is important for anyone trying to help or deal with it. As I said, for me it was extreme stress. For others it comes from social pressures affecting self esteem, or some kind of unhealthy relationship with food.
For the pp asking about helping daughter, whatever you do don't get angry with her or shout. That get's nowhere and alienates you further. It's better to be on the inside with her. Let her talk to you about it and explain if she can. Ask questions rather than say eat more. That way you are an ally.
It's also good to develop a positive relationship with food. I have a healthy vegan diet (maybe better for someone a bit older and not a teenager) and get healthy exercise, yoga is a good one for body and mind if your DD is old enough, or something she is interested in? I have to eat to be able to move and be physically strong, I choose to do this without having to convince myself, plus I feel and look good, so I love my body rather than hate it as many people with ED may do.
Maybe healthy eating, learning to cook healthy meals at home? There's no need to go straight to previous eating habits or similar to your own/rest of family, because at first a regular portion will seem like a mountain and a bit disgusting. So eating something, a small portion that you openly say ok lets have just a small portion then, or soup, something that doesn't get alarm bells ringing in her head, and lots of support and praise if she does. Gradually I remembered how much I loved food and was able to eat lots without finding it strange anymore!
I'd say try to get her to take vitamins and supplements (a specialist maybe can advise), one thing I don't like is that my body missed out of these for a time.
Therapy of course is the obvious thing to advise, but there are things you can try at home. Try to stay calm about it with her, talk gently like an adult conversation so maybe she'll open up about how she feels and trust you to be talking to her, not forcing her to do anything. If you are on her side and she feels that, she may take little steps with you at her side.