What to expect when I tell my adoptive parents

I have recently, within the last week, located both of my birth parents. I hired a search agency, and they made the initial contact to each parent, and they both indicated they did want me to contact them. The reception I received from my birth mom was somewhat "unenthusiastic", so I am unsure how much additional contact I will have with her, and I am actually completely ok with that, since I do consider my adoptive parents my "mom and dad". However, my birth father told me that he never wanted the adoption, and that he has thought about me every day in the past 42 years, and he definitely wants to meet me. I also have a half sister who has known about me all her life, and wants to meet me also. I am struggling with how I go about telling my adoptive parents about all this, and have some concerns about how they may react. I don't want to cause problems with my relationship with them, but also very much want to meet my birth father and half sister, and possibly continue to stay in touch with them. Anybody out there who has been in my position, if you could please tell me how you went about telling your adoptive parents, and how your new relationships with your birth family have impacted your relationship with your adoptive parents, I would greatly appreciate it.