We are planning to use Azure Front door for Azure App Service (web app) and planning to use APIM which may not need to expose externally or to public directly. Only the Azure Web app is going to call the API's via APIM.
In the above scenario,
- Do we need Azure front door to connect with both App service and APIM
- Connect Azure Front door only to App service. And app service can connect to APIM.
In the scenario you have described you will be able to connect Front Door to your Web App. Front Door will not need access to or need to know about the API Management instance.
If you wanted to expose your APIs publicly you could certainly do that, but it sounds like you'll want to keep them firewalled off from the public internet and only allow your Web App to access them.