Solution

First, find the point of intersection (Q):

We know point P by inspection:

So, the equation for the line is:

This has an extra set of curly brackets (and that will matter later), but we can fix that by using Flatten:

So, now for the grand finale...  As ,

I have to admit that this didn't fit in with my initial guess about what would happen (why 4?).  So, to help visualize this, I set up an animation:

The errors are due to round-off induced division by 0 (i.e., not really a problem).  However, this animation looks lousy.  Even after explicitly giving a PlotRange (usually this fixes the "jumpiness" here), it still jumps around all over the place.  (I consider this a bug in Mathematica; it isn't actually doing what I asked it to.)  However, you can fix this by using the command ShowAnimation (this is why I named the above animation):