(*Example 9 *)
Clear[x,y,lptxt,lptyt,pm1,pm2];
x[t_]:=2t+3;
y[t_]:=t^2–1;
prp=ParametricPlot[{x[t],y[t]},{t,0,10},PlotRange->{{0,30},{0,100}}];
lpt[t_]:=ListPlot[{{x[t],y[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},PlotRange->{{0,30},{0,100}},AxesLabel->{"x","y"}];

lptxt[t_]:=ListPlot[
{{t,x[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},
PlotRange->{{0,10},{0,30}},AxesLabel->{"t","x"}
];

lptyt[t_]:=ListPlot[
{{t,y[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},
PlotRange->{{0,10},{0,100}},AxesLabel->{"t","y"}
];

pm1:=Manipulate[
{
Show[{lptxt[t],Plot[x[tt],{tt,0,10}]}],
Show[{lptyt[t],Plot[y[tt],{tt,0,10}]}],Show[{lpt[t],prp}]
},{t,0,10,0.1}];
Print[pm1]

(*Example 10 *)
Clear[x,y,lptxt,lptyt,pm1,pm2];
x[t_]:=Sqrt[t]
y[t_]:=t;
prp=ParametricPlot[{x[t],y[t]},{t,0,10}
(*,PlotRange->{{0,30},{0,100}}*)
];
lpt[t_]:=ListPlot[{{x[t],y[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},PlotRange->{{0,5},{0,10}},AxesLabel->{"x","y"}];

lptxt[t_]:=ListPlot[
{{t,x[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},
PlotRange->{{0,10},{0,20}},AxesLabel->{"t","x"}
];

lptyt[t_]:=ListPlot[
{{t,y[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},
PlotRange->{{0,10},{0,20}},AxesLabel->{"t","y"}
];

pm1:=Manipulate[
{
Show[{lptxt[t],Plot[x[tt],{tt,0,10}]}],
Show[{lptyt[t],Plot[y[tt],{tt,0,10}]}],Show[{lpt[t],prp}]
},{t,0,10,0.1}];
Print[pm1]

Clear[x,y,lptxt,lptyt,pm1,pm2];
(*Example 12 *)
x[t_]:=Cos[t];
y[t_]:=Sin[t];
trange={0,2Pi};yrange={-1,1};xrange={-1,1};

prp=ParametricPlot[{x[t],y[t]},{t,0,10},PlotRange->{xrange,yrange}];

lpt[t_]:=ListPlot[{{x[t],y[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},PlotRange->{xrange,yrange},AxesLabel->{"x","y"},AspectRatio->1];

lptxt[t_]:=ListPlot[
{{t,x[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},
PlotRange->{trange,xrange},AxesLabel->{"t","x"}
];

lptyt[t_]:=ListPlot[
{{t,y[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},
PlotRange->{trange,yrange},AxesLabel->{"t","y"}
];

pm2:=Manipulate[
{
Show[{lptxt[t],Plot[x[tt],{tt,0,2Pi}]}],
Show[{lptyt[t],Plot[y[tt],{tt,0,2Pi}]}],Show[{lpt[t],prp}]
}
,{t,0,2Pi,0.1}];

Print[pm2];

Clear[x,y,lptxt,lptyt,pm1,pm2];
(*Example heart *)
x[t_]:=16Sin[t]^3;
y[t_]:=13Cos[t]-5Cos[2t]-2Cos[3t]-Cos[4t];

trange={-20,20};yrange={-20,20};xrange={-20,20};

prp=ParametricPlot[{x[t],y[t]},{t,0,10},PlotRange->{xrange,yrange}];

lpt[t_]:=ListPlot[{{x[t],y[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},PlotRange->{xrange,yrange},AxesLabel->{"x","y"},AspectRatio->1];

lptxt[t_]:=ListPlot[
{{t,x[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},
PlotRange->{trange,xrange},AxesLabel->{"t","x"}
];

lptyt[t_]:=ListPlot[
{{t,y[t]}},PlotLabel->"t="<>ToString[t],PlotStyle->{PointSize->0.1,Red},
PlotRange->{trange,yrange},AxesLabel->{"t","y"}
];

pm2:=Manipulate[
{
Show[{lptxt[t],Plot[x[tt],{tt,0,2Pi}]}],
Show[{lptyt[t],Plot[y[tt],{tt,0,2Pi}]}],Show[{lpt[t],prp}]
}
,{t,0,2Pi,0.1}];

Print[pm2];

parametric plot showing space curve of a vector whose terminal is  described by
 r[t] = x[t] i + y[t] j + z[t] k; The red-colored arrows is the tangent vector to the space curve.

x[t_]:=Sin[t];
y[t_]:=Cos[t];
z[t_]:=t/5.0;
r[t_]:={x[t],y[t],z[t]};

g0:=ParametricPlot3D[r[t],{t,-10,10}];
g1[t_]:=Graphics3D[
{Arrow[{{0,0,0},r[t]}]},AspectRatio->1,Axes->True,PlotRange->{{-1,1},{-1,1},{-1,1}}];
g2[t_]:=Graphics3D[
{PointSize->Large,Point[{{0,0,0},r[t]}]},AspectRatio->1,Axes->True,PlotRange->{{-1,1},{-1,1},{-1,1}}];

vec[dumm_]:=D[r[t],t]/.{t->dumm};
g3[t_]:=Graphics3D[{Red,Arrow[{r[t],r[t+0.3]}]},AspectRatio->1,Axes->True,PlotRange->{{-1,1},{-1,1},{-1,1}}];

Manipulate[Show[{g0,g1[t],g2[t],g3[t]}],{t,-10,10,0.1}]