The biggest thing to remember is don't do anything you're not comfortable with. You say that you're not depressed, but are anxious? So maybe a good way to start would be to let them know that you're not depressed or suicidal, but the anxiety that they already know about is to a point that this is the only way you could think to deal with it. I don't know your exact situation, but if it was me, that's what I'd say.
You should be proud of yourself, this is a big step! Depending on how your parents take it, it might even make things a little easier on you at home. For me personally, my mom knows, and there's days that I'm glad she knows and others that I wish I never would have said anything.
Best of luck to you!! =]
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