I don't know what to do, need help coming out to my dad and society

Hallo again everyone! I usually wouldn't post this here but I actually need help and my site doesn't get much traction...
So I'm trans as you probably know and while my mom kinda knows, my dad (I think) doesn't know and I don't know how to come out, he's a very supportive parent but he has said some things about gay and trans people in the past (mainly referring to them with the t-slur, all the damn time) so I don't know how it would pan out, like I said my mom knows and she told me that if I simply told him straight up decisively he'd just accept it but I don't know if that's entirely true... I need him to know so he doesn't find out on his own because if that ever happened I know the backlash would be nuclear. 

I need his approval in order to battle my own social demons which are coming with the new school year, I'm going to a new school for a computer science degree (dunno the equivalent in american) and I'm kind of scared I'll be fucked over by having to bottle up my femininity every day for 6 hours and pretend to be someone I'm not just to get accepted into a social group. I'm crafty socially, I can make do with only 1 friend but having no one on your side will for sure be a problem. I don't know what to do, please help me because I'm at a loss right now, I have 3 weeks until the new year starts and I'm scared shitless that I'll have to come out to my dad and to the entirety of society in only 3 weeks...