"Sample code: Using ParametrixPlot[] and Show[] to display the locus / trajectories of circles and its center located at C(h,k)";
h=2;k=3;
T=1;R=1;omega=2Pi/T;
x[t_]:=R*Cos[omega*t]+h;y[t_]:=R*Sin[omega*t]+k;
prp1=ParametricPlot[{x[t],y[t]},{t,0,T}];
pp2=Graphics[{PlotStyle->{Blue,PlotMarkers->"X"},PointSize->0.03,Point[{h,k}]}];
Show[{prp1,pp2}]