How to host a REST API with a domain/website?

I'm a beginner when it comes to stuff like this but I have a question(s) I want to ask.

I'm trying to host a website and a API, my question is how do I do this?

Here's an example of what I'm trying to achieve; As "main" site/front page: https://nekobot.xyz/

And as GET url: https://nekobot.xyz/api/image?type=coffee

Do I need separate hosting for my API as well as my website?

I've already made an API that work like the one mentioned above, but that is on a local machine, I'm not sure how to combine the API and Website into one like the example I showed.

Sorry if I didn't explain it very well, like I said I'm a total beginner when it comes to this. Hopefully there's someone who can bring some clarity.