ParametricPlot[{t,t^2},{t,-5,5}]

ParametricPlot[{Cos[t],Sin[t]},{t,0,Pi}]

ParametricPlot[{Sin[t],Cos[t]},{t,0,Pi}]

ParametricPlot3D[{5Cos[t],5Sin[t],t},{t,0,6 Pi}]

ParametricPlot3D[{1+2t,3-t,5+3t},{t,-5,5}]

ParametricPlot[{3+2Cos[t],2+2Sin[t]},{t,0,3Pi/2}]

ParametricPlot[{3+2Sin[t- Pi/2],2+2Cos[t- Pi/2]},{t,0,3Pi/2}]

sphere=ContourPlot3D[x^2+y^2+z^2==81,{x,-10,10},{y,-10,10},{z,-10,10}];
line=ParametricPlot3D[{t,2t,2+3},{t,-5,5},PlotStyle->{Black,Thickness[.02]}];
Show[line,sphere]

ParametricPlot3D[{{t,1+2t,3-2t},{-2-2t,1-2t,1+t}},{t,-5,5}]

ParametricPlot3D[{{t-1,1+2t,5-t},{2+2t,4+t,3+t}},{t,-5,5}]

circle=ParametricPlot[{Cos[t],Sin[t]},{t,0,2Pi}];
arrows=Graphics[{Thickness[.01],Arrow[{{1,0},{1,1}}],Arrow[{{Sqrt[2]/2,Sqrt[2]/2},{0,Sqrt[2]}}]}];
points=Graphics[{PointSize[.04],Point[{1,0}],Point[{Sqrt[2]/2,Sqrt[2]/2}]}];
Show[circle,arrows,points,PlotRange->{{-1,1},{-1,2}}]

graph=ParametricPlot3D[{t^2,t^3,2t},{t,0,3}];
arrows=Graphics3D[{Thickness[.01],Arrow[{{4,8,4},{8,20,6}}]}];
points=Graphics3D[{PointSize[.04],Point[{4,8,4}]}];
Show[graph,arrows,points,PlotRange->Automatic]

circle=ParametricPlot[{Cos[t],Sin[t]},{t,0,2Pi}];
arrows=Graphics[{Thickness[.01],Arrow[{{1,0},{0,0}}],Arrow[{{Sqrt[2]/2,Sqrt[2]/2},{0,0}}]}];
points=Graphics[{PointSize[.04],Point[{1,0}],Point[{Sqrt[2]/2,Sqrt[2]/2}]}];
Show[circle,arrows,points,PlotRange->{{-1,1},{-1,2}}]