ParametricPlot[{t^2, t^3}, {t, -3, 3}]

ParametricPlot[{t^2, t^3}, {t, -3, 3}, PlotRange -> {{-10, 10}, {-10, 10}}]

ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2Pi},PlotRange -> {{-2, 2}, {-2,2}}]

ParametricPlot[{{t^2, t^3},{Cos[t], Sin[t]}}, {t, -2Pi,2Pi}, PlotRange -> {{-10, 10}, {-10, 10}}]

Show[{ParametricPlot[{t^2, t^3}, {t, -3, 3}, PlotRange -> {{-10, 10}, {-10, 10}}], ParametricPlot[{Cos[t], Sin[t]}, {t, -2Pi,2Pi}, PlotRange -> {{-5, 5}, {-5, 5}}]}]

Show[{ParametricPlot[{t^2, t^3}, {t, -3, 3}, PlotRange -> {{-10, 10}, {-10, 10}}], ParametricPlot[{Cos[t], Sin[t]}, {t, -2Pi,2Pi}, PlotStyle-> Green, PlotRange -> {{-5, 5}, {-5, 5}}]}]

Show[{ParametricPlot[{t^2, t^3}, {t, -3, 3}, PlotRange -> {{-10, 10}, {-10, 10}}, PlotStyle->Dashed], ParametricPlot[{Cos[t], Sin[t]}, {t, -2Pi,2Pi}, PlotStyle-> {Green,Thick},  PlotRange -> {{-5, 5}, {-5, 5}}]}]

Manipulate[ParametricPlot[{Cos[t], Sin[t]}, {t, 0, k},PlotRange -> {{-2, 2}, {-2,2}}], {k, 0.1, 2Pi}]

Manipulate[ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2Pi},Epilog -> {Red, PointSize[Medium], Point[{Cos[k], Sin[k]}]},PlotRange -> {{-2, 2},(*gsdhksdghsdkjsdhjkdgs*) {-2,2}}], {k, 0.1, 2Pi}]

Manipulate[ParametricPlot[{Cos[k*t],Sin[t]}, {t, 0, 6Pi}, PlotRange -> {{-2,2}, {-2,2}}], {k, 1, 6}]

ParametricPlot[{Sin[t],Cos[t]+Log[Tan[t/2]]}, {t,0, Pi}, PlotRange -> {{-1,1},{-3,3}}]

Manipulate[ParametricPlot[{Sin[t],Cos[t]+Log[Tan[t/2]]}, {t,0, Pi}, PlotRange -> {{-1,1},{-3,3}}, Epilog -> {Red, Line[{{Sin[k], Cos[k]+Log[Tan[k/2]]},{0, Cos[k]+Log[Tan[k/2]]+(1/2 Csc[k/2]Sec[k/2]-Sin[k])*(-Tan[k])}}]}], {k, 0.01, Pi}]

ellisse[x0_,y0_][a_,b_][t_]:= {x0+a*Cos[t], y0+b*Sin[t]}

ParametricPlot[ellisse[2,4][7,3][t], {t,0,2Pi}, PlotRange -> {{-15,15},{-15,15}}]