Answer
$$r(t)=\lt 2+\cos t,-1+\sin t,4\gt.$$
Work Step by Step
We know that the unit sphere centered at $(2,-1,4)$ has the equation
$$(x-2)^2+(y+1)^2+(z-4)^2=1.$$
Its horizontal projection on the xy-plane is $$(x-2)^2+(y+1)^2 =1.$$
So we get the parametrization $$x=2+\cos t, \quad y=-1+\sin t, \quad z=4.$$
That is $$r(t)=\lt 2+\cos t,-1+\sin t,4\gt.$$
