Struggling with coming out

I'm age 13 and am a lesbian. I don't quite know how to come out to my parents. I just recently heard a conversation and found out that my mom is homophobic. She doesn't want any children in her household to be gay. I was feeling comfortable with coming out until that moment. I have no clue what to do and I am scared that my mom will hate me for who I am. Any suggestions on what I should do?