a={1,0,2};u=(1/(Sqrt[14])){1,2,3}; v=(1/(3(Sqrt[3]))){5,-1,-1}; 

Graphics3D[{{Blue,Table[Point[a+Cos[t] u+Sin[t] v],{t,0,2 Pi,(1/128)}]},{Red,Table[Point[Cos[t] u+Sin[t] v],{t,0,2 Pi,(1/128)}]}},PlotRange->{{-2,2},{-2,2},{-2,2}},AxesLabel->{x,y,z},Boxed->True,Ticks->Automatic]

Options[Graphics3D]

ParametricPlot[t{1,0}+Sin[t]{0,1},{t,-2Pi,2Pi},PlotRange->{{-2 Pi,2Pi},{-2 Pi,2Pi}},AspectRatio->Automatic,ImageSize->200]

Manipulate[ParametricPlot[{1,2}+t{Cos[θ],Sin[θ]}+Sin[t]{-Sin[θ],Cos[θ]},{t,-2Pi,2Pi},PlotRange->{{-2 Pi,2Pi},{-2 Pi,2Pi}},AspectRatio->Automatic,ImageSize->200],{θ,0,2 Pi}]

Manipulate[Show[Table[ParametricPlot[t{Cos[θ+s],Sin[θ+s]}+Sin[t]{-Sin[θ+s],Cos[θ+s]},{t,-3Pi,3Pi},PlotRange->{{-2 Pi,2Pi},{-2 Pi,2Pi}},AspectRatio->Automatic,ImageSize->200],{θ,0,2 Pi,((2 Pi)/64)}]],{s,0,2Pi}]

ParametricPlot3D[t{1,0,0}+Sin[t]{0,0,1},{t,0,2Pi},PlotRange->{{-2 Pi,2Pi},{-2 Pi,2Pi},{-2 Pi,2Pi}},AspectRatio->Automatic,ImageSize->200]

Manipulate[ParametricPlot3D[t{Cos[θ],Sin[θ],0}+Sin[t]{0,0,1},{t,0,2Pi},PlotRange->{{-2 Pi,2Pi},{-2 Pi,2Pi},{-2,2}},BoxRatios->{1,1,1},ImageSize->200],{θ,0,2 Pi}]

ParametricPlot3D[t{Cos[θ],Sin[θ],0}+Sin[t]{0,0,1},{t,0,2Pi},{θ,0,2Pi},PlotRange->{{-2 Pi,2Pi},{-2 Pi,2Pi},{-2,2}},BoxRatios->{1,1,1},ImageSize->200]