It is the first time I post a Maple bug in MaplePrimes because I use to submit an SCR.
There is a serious reason to do so. Let us look at the output of
> implicitplot(sqrt(x^2+y^2)-sqrt((x-4)^2+(y-3)^2) = 5, x = -20 .. 20, y = -20 .. 20,
numpoints = 10^6, thickness = 5, scaling = constrained);
(both in Maple 13 and in Maple 16)
The expected plot is the ray from the point (4,3) to infinity along the line y=3/4*x
in the positive quadrant. I do not find any workaround.