aa=1;bb=2;cc=3;a1=-3;b1=1;c1=-2;Manipulate[Show[ContourPlot[aa x+bb y+cc==0,{x,-5,5},{y,-5,5},ContourStyle->{Blue}],ContourPlot[a1 x+b1 y+c1==0,{x,-5,5},{y,-5,5},ContourStyle->{Red}],ContourPlot[(s aa +t a1) x+(s bb + t b1) y+(s cc+t c1)==0,{x,-5,5},{y,-5,5},ContourStyle->{Green}],ImageSize->300],{{s,1},-1,1},{{t,1},-1,1}]

Show[Plot[Table[α x +(1/α),{α,.1,13,.1}],{x,-7,7},PlotStyle->{GrayLevel[.8]}],Plot[Table[-α x +(1/(-α)),{α,.1,13,.1}],{x,-7,7},PlotStyle->{GrayLevel[.8]}],ParametricPlot[{((y^2)/4),y},{y,-6,6}],AspectRatio->Automatic,PlotRange->{{-6,6},{-6,6}}]

Show[Plot[Table[((-1)/(2 α)) (x-α) +(α^2),{α,.1,13,.05}],{x,-7,7},PlotStyle->{GrayLevel[.8]}],Plot[Table[(1/(2 α)) (x+α) +(α^2),{α,.1,13,.05}],{x,-7,7},PlotStyle->{GrayLevel[.8]}],ParametricPlot[{x,x^2},{x,-6,6}],ParametricPlot[{x,(1/2)+3((((x/4)^(2)))^(1/3))},{x,-9,9}],AspectRatio->Automatic,PlotRange->{{-6,6},{-6,6}}]