Chasing Person B: Describing the Curve Mathematically

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hypermonkey2
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Heres a problem that could use some light. Say person A at (0,1) is following a person B at (0,0). Person B moves horizontally with a constant speed v (towards the positive x direction). Person A also moves with speed v, but always in the direction pointing at person B (to chase him). How can we describe mathematically the curve thus created?

I hope my explanation of the problem was clear, thanks!
 
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I wouldn't think so. Their distance might become infinitely small though, if that means the same thing.
 
That would seem to be the case. But even so, we haven't been able to solve the differential equation. Can you try a mathematical analysis? This is not homework, haha, no need for the socratic method.
 
Have a look at http://mathworld.wolfram.com/PursuitCurve.html" .
 
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thanks, ill wrestle with that.