For the two curves use the command:

    g1 = ParametricPlot3D[{{t, 0, t^2}, {0, u, u^2}}, {t, -10,10}, {u, -10, 10},
         BoundaryStyle -> Thick];

in addition, if you want also to have the two $x-y$ and $y-z$ planes in the plot:

    planes = ContourPlot3D[{x == 0, y == 0}, {x, -10, 10}, {y, -10, 10}, {z,0, 100}, 
             Mesh -> False, ContourStyle -> {Directive[Blue, Opacity[0.4]], 
             Directive[Green, Opacity[0.4]]}];

    Show[g1,planes,PlotRange->{All,All,{-10,10}}]
>![enter image description here][1]


  [1]: https://i.sstatic.net/l0Kgu.png