Aug 5 (Reuters) - European Wax Center Inc, a franchiser and retailer of waxing services and products backed by General Atlantic, was valued at $1.2 billion in its Nasdaq debut on Thursday as shares rose 12%. The stock opened at $19 on Thursday, compared with the initial public offering price of $17. Reporting by Sohini Podder in Bengaluru; Editing by Aditya Soni Our Standards: The Thomson Reuters Trust Principles.