How do I tell my mom I want to try and talk to my dad

[distant ledge]

Ok, this is a long one so I'll throw a quick rundown of everything at the end.

My parents broke up before I was born, so from the start pretty much (not sure how old I was when I started to) I would go see my dad for a week / weekend or whatever in a town like 2 hours away from where I was born & lived.
My dad tried to get full custody, and apparently did some sneaky shit, but I'm the end they ended up with 50/50 custody of me.
The visits continued as normal until I was around 3.5 years old and then my dad began to make excuses as to why he couldn't take me for his time, before he eventually just stopped responding to calls or texts at all.
Now, I'm 17, turning 18 this year, and we haven't heard a word from him since, and he's never paid a dime of child support.
(He also has 2 other daughters, and a son, my half siblings. They're all Iike in their mid 20s now and my sisters both have 1-2 kids, we discovered this through Facebook.)
Spring / summer of last year, we were visiting my aunt & cousin when my dad came up in the topic of conversation and my mom and aunt ended up looking for him on Facebook and Instagram, and they found him so I tried looking and found nothing. Whatever, I'll just move on right? Nah, every once in a while I looked again out of curiosity and found nothing.
I don't recall why, but my half siblings came up as the topic of a conversation my mom and I were having last summer, and she wound up showing me their Facebook pages, and she told me if I wanted to I could reach out. I didn't, but over the next months would scroll through their accounts trying to find pictures of my dad.

Early January this year, I was looking at a post one of my sisters made on fathersday a few years back, and noticed their was a comment on it that I couldn't see, so I made another account to see if that made a difference, and when I checked it was him. His account was under his middle name so it wasn't obvious until I checked his account and saw it was definetly him and not some uncle or something.
So, eventually I showed my mom, who showed my stepdad. Well, it was a good thing I saved all the photos and videos of him to my phone, because my stepdad got the bright idea of making a fake account and messaging him, basically calling him a piece of shit anonymously. He also messaged my sister and told her to ask her dad why he abandoned his sister.
He thought about it a few hours later and deleted the messages and account. However it was too late, one of them must have seen it because the next morning my dad's account was gone and my sisters is private now.
I told then this when I got home from school that day and we ended up having a conversation and they basically told me it's ok to be curious and it's my choice if I want to try to talk to him. After that we moved on and didn't talk about it again.
Since then, I've been thinking about my dad every day and I really want to try to reach out even if he just ignores me, because he may not deserve to know me, but I deserve to know him. Know what my own dad's voice sounds like. And it's really been effecting my mental health.
I plan on telling my mom I want to try and reach out tomorrow night, but I don't want to hurt her feelings or something (anxiety) and I don't know how to tell her... my friends have tried to give advice but they're the kind of person that doesn't see how this is that hard haha.
Advice greatly appreciated

TL:DR -
My dad left when I was 3, now I'm 17 and found him on Facebook, I wanna reach out but don't know how to tell my mom cause he put her thru a lot of shit.
Looking for advice.