I am writing a .NET application that uses cookies to store a login token.  I'd like the user to be able to log into multiple installations of this application on the same server (let's say jacob.local/Devel and jacob.local/Stable), so I want to set the Path property for the cookies appropriately.  Currently I'm using Request.ApplicationPath but am running into trouble when the user visits the site with a different case than what I've set up in IIS.
For example, the user visits jacob.local/stable -- the cookie's path will be /Stable, which the browser doesn't send back to me since it can't know that IIS is case insensitive.
Do I have to parse apart the whole query string myself, or is there already a function for figuring out what the path of the application is?