ParametricPlot[{t^2+1, t^3+2}, {t, -5, 5},PlotRange->10]

Show[%88,ImageSize->Tiny]

ParametricPlot[{t^2+1, t^3+2}, {t, -5, 5},PlotRange->10, Axes -> None]

ParametricPlot[{{t^2+1, t^3+2}, {-t^3,2t}}, {t, -5, 5},PlotRange->10]

Show[{ParametricPlot[{t^2+1, t^3+2}, {t, -5, 5},PlotRange->10], ParametricPlot[{Exp[t] ,t^3+2}, {t, -2, 2}, PlotStyle-> {Red}]}]

ContourPlot[x^2/3+y^2/9==1, {x,-3,3},{y,-3,3}]

ContourPlot[x^3*y+2x*y^5+y^2==1, {x,-10,10},{y,-10,10}](*jfssajkhfkajsh*)

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

ParametricPlot[ellisse[2,3][2,5][t], {t,0, 2Pi}, PlotRange->8]

Manipulate[ParametricPlot[ellisse[2,3][2,5][t],{t,0.01,k}, PlotRange->8], {k, 0, 10Pi}]

Manipulate[ParametricPlot[ellisse[2,3][k,5][t],{t,0,2Pi}, PlotRange->8], {k, 0.1, 6}]

vt[gamma_] := Simplify[D[gamma[tt],tt]]/.tt-> t

nvt[gamma_][t_] :=Sqrt[Simplify[D[gamma[tt],tt].D[gamma[tt],tt]]]/.tt-> t

lung[a_,b_][gamma_] :=Integrate[nvt[gamma][u],{u, a,b}]

lemniscata[t_]:={Cos[t]/(1+Sin[t]^2), Sin[2t]/(1+Sin[t]^2)}

parabola[t_] := {t,t^2}

ParametricPlot[lemniscata[t], {t, 0, 2Pi}]

lung[0,1][parabola]

retta[t_]:= {t, 3t}

lung[0,1][retta]

lung[1,2][lemniscata]