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 the two $x-y$ and $y-z$ planes:
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}}]
