Unless they ask specifically for it, the answer is no.
Usually, the question is "Find the equation of the locus and describe it" or something along those lines.
In the example that you gave above, I would say: The locus is a circle centred at (1,-3) with radius 2.
You only need to define DISTINCTIVE features such as a centre/radius if its a circle, the focal length if its a parabola etc.