SetDirectory["C:\\Users\\david\\Documents\\My Dropbox\\elte\\5. felev\\elmmech\\7"];

Plot[Table[i,{i,0,10}],{x,-5,5}]

a=2;

e==(m/2)((Subscript[v, 0])^2)==(m/2)((Subscript[v, 1])^2)-(Subscript[V, 0])

Solve[((m (Subscript[v, 0]^2))/2)==((m (Subscript[v, 1]^2))/2)-(Subscript[V, 0]),(Subscript[v, 1])]

c=((((((Sqrt[2]) (Sqrt[(1/2) m (Subscript[v, 0]^2)+(Subscript[V, 0])]))/(Sqrt[m]))))/(Subscript[v, 0]))

c=((Subscript[v, 1])/(Subscript[v, 0]));

c=0.8;

m[i_]:=Tan[ArcSin[i/(a*c)]-ArcSin[i/a]]

(Subscript[x, 0])[i_]=-Sqrt[(a^2)-(i^2)];

tortfeny=Table[m[i]*x+i-(Subscript[x, 0])[i]*m[i],{i,-2,2,0.1}];

tortWoI[i_]:=m[i]*x+i-(Subscript[x, 0])[i]*m[i]

Plot[{tortfeny,(Sqrt[4-(x^2)]),-(Sqrt[4-(x^2)])},{x,-5,0},PlotStyle->Thickness[0.0001]]

Plot[{Table[Piecewise[{{Tan[ArcSin[i/(a*c)]-ArcSin[i/a]]*x+i+Sqrt[(a^2)-(i^2)]*Tan[ArcSin[i/(a*c)]-ArcSin[i/a]],x<-Sqrt[(a^2)-(i^2)]},{i,x>-Sqrt[(a^2)-(i^2)]}}],{i,-2,2,0.05}],(Sqrt[4-(x^2)]),-(Sqrt[4-(x^2)]),Table[i,{i,2,2.3,0.05}],Table[i,{i,-2.3,-2,0.05}]},{x,-12,0},PlotStyle->Thickness[0.0001]]

Export["vizual.png",,ImageSize->{3000,3000},ImageResolution->600]