Map client to alternate virtual directory based on url prefix?

I have an app that has an external url that is different from the internal url.  Lets refer to them as:

https://external.app.com/virtualdir/app.exe   (uses to forms based authentication)

and

http://internal.app.com/virtualdir/app.exe   (uses integrated authentication)

Currently the external url is being served up via a lightweight proxy which we plan to eliminate in favor of a direct connection via an F5 device.  

However, on the iis7 webserver (server 2008), /virtualdir is set to integrated authentication.  Is there a way to detect that the client is using "external.app.com" and map them to the forms based virtual directory,  /virtualdirforms for example, all while keeping the /virtualdir url syntax on the client?  

I know I can create a new website on the server and create another /virtualdir with forms based authentication set, but from what I gather, it would require another IP to be allocated to the server, which would require I jump through a bunch of red tape that I don't want to do.

Hopefully this makes sense, I can clarify if need be.
bmsandeAsked:
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Mohammed KhawajaManager - Infrastructure:  Information TechnologyCommented:
No additional IP is needed.  What you could do is bind the site not to IP address but to name.

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Dan McFaddenSystems EngineerCommented:
To clarify more... You can run multiple websites on a single IIS server which has only 1 IP address by utilizing Host Names on the website binding.

http site binding on port 80 with a host name configured.
You can also create an internal site only, add a virtual directory to this site and point it to the same physical path that the external app virtual directory points to.  Now you can control the authentication method to the virtual directory which points to the same code.

Dan
bmsandeAuthor Commented:
This is exactly what I needed.  Worked perfectly.  Thanks.
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