EventHorizon
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EventHorizon's post in Miscellaneous logic puzzle from exam was marked as the answer
I looked at that for a while. Though it's not much, here's what I got...
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EventHorizon's post in Interesting one - A Cat and A mouse was marked as the answer
(Hint: don't look for the curve, just examine the distance between them and how it changes with time)
I'll try (again) to find the equation for the path in a bit.
Edit: I thought I'd include the last equation I got, but kept failing to verify. So I don't know it if is correct.