(* Sample code 1: Parametric plot of an ellipse. Mark a few points on the plot using ListPlot[{{x,y}}] *)
a=0.5;b=.75;h=0.75;k=5;T=2Pi;
x[t_]:=h+a Cos[t];
y[t_]:=k+b Sin[t];
pp=ParametricPlot[{x[t],y[t]},{t,0,2Pi}];
lp1=ListPlot[{{h,k}},PlotStyle->PointSize[0.05]];
lp2=ListPlot[{{x[0.5T],y[0.5T]}},PlotStyle->PointSize[0.05]];
Show[{pp,lp1,lp2}]

(* Sample code 2: Simulate the circulation of a point around the ellipse.*)
a=0.5;b=.75;h=0.75;k=5;T=2Pi;
x[t_]:=h+a Cos[t];
y[t_]:=k+b Sin[t];
pp=ParametricPlot[{x[t],y[t]},{t,0,2Pi}];
lp1=ListPlot[{{h,k}},PlotMarkers->"×"];
lp2[t_]:=ListPlot[{{x[t],y[t]}},PlotStyle->PointSize[0.05]];
Manipulate[Show[{pp,lp1,lp2[t]}],{t,0,T,0.01T}]

(*Sample code 3: (a) Customize ListPlot of two points P1={x1,y1};P2={x2,y2};
(b) Draw a line between two points using Graphics[Line[{P1,P2}]]; (c) Combine both using Show[{,}]*)

PP1={1,2};PP2={2,4};
lp=ListPlot[{PP1,PP2},PlotMarkers->{"×",Large}]
gll=Graphics[Line[{PP1,PP2}]]
Show[{lp,gll}]

a=0.5;b=.75;h=0.75;k=5;T=2.0Pi;
x[t_]:=h+a Cos[t];
y[t_]:=k+b Sin[t];
pp=ParametricPlot[{x[t],y[t]},{t,0,2Pi}];
lp1=ListPlot[{{h,k}},PlotMarkers->"×"];
lp2[t_]:=ListPlot[{{x[t],y[t]}},PlotStyle->PointSize[0.05]];
Manipulate[Show[{pp,lp1,lp2[t]}],{t,0,T,0.01T}]