Animate[Show[ParametricPlot[{Cos[t],Sin[t]},{t,0,2Pi}],ParametricPlot[{3/4Cos[t]+1/4*Cos[3t],3/4*Sin[t]-1/4*Sin[3t]},{t,0,x}, PlotRange->{{-1.1,1.1},{-1.1,1.1}},PlotStyle->Red], Graphics[{Red,PointSize[Medium],Point[{3/4Cos[x]+1/4*Cos[3x],3/4*Sin[x]-1/4*Sin[3x]}]}],ParametricPlot[{3/4Cos[x]+1/4*Cos[t],3/4*Sin[x]-1/4*Sin[t]},{t,0,2Pi}, PlotRange->{{-1.1,1.1},{-1.1,1.1}},PlotStyle->Black]],{x,0,2Pi}]