How to convince my parents to let me go to the gym?

Hi, so I'm 17 years old asian girl, turning 18 years in old in a month time and I want to enter the Australian Defence Force.

My parents support me wholeheartedly about my idea and I want to prepare myself for the army in terms of my physical abilities.

Truthfully, I'm not a very physical person so now I'm starting to exercise here and there but I kinda want to take it to another level, which is gym.

We have an elliptical machine in my house and I've been using it regularly, but I feel like I need to do more exercises than that and gym most likely would have a lot more equipment. I know my dad will go against me going to the gym because we have that machine and I don't know what to say. He's a stubborn man.

So, help?

Thanks