Does my company really own every idea I come up with?

From Hacker News:

I work for a large company that owns a website with a couple million members that allows them to get answers to their technical questions, read blogs, network with their peers, etc from that website. I am a salaried mid-level .NET developer at work during the day.

I came up with an idea for a web app that could really take off. I’ve been working on it at home, on my own machine, on my own time. Its written in Python using the Google App Engine SDK (super awesome, BTW). I can see needing Angel or VC funding at some point, or selling it if it really does take off (that would be my ultimate goal, of course — selling it to a larger company and cashing out).

My concern is, since I work for this larger company and signed an “Employer Protection Agreement” when I was hired, do they own my “invention” (web app), even though it was developed on my own time, with my own resources? Where is the line between whether a web app relates to my current employer’s site or not.