Show[ContourPlot[x^2+y^2,{x,-4,4},{y,-4,4},ContourShading->None],ContourPlot[x^2y-16==0,{x,-4,4},{y,-4,4},ContourStyle->Red]]

Show[ContourPlot[y,{x,-4,4},{y,-4,4},ContourShading->None],ContourPlot[y^3-x^2==0,{x,-4,4},{y,-4,4},ContourStyle->Red]]

Show[ContourPlot3D[x y+2z,{x,-4,4},{y,-4,4},{z,-4,4}],ContourPlot3D[x+y+z==0,{x,-4,4},{y,-4,4},{z,-4,4}]]

Show[
ContourPlot3D[x y+2z,{x,-4,4},{y,-4,4},{z,-20,20},Contours->{12}],
ContourPlot3D[x+y+z==0,{x,-4,4},{y,-4,4},{z,-20,20},Contours->{12}],
ContourPlot3D[x^2+y^2+z^2==24,{x,-4,4},{y,-4,4},{z,-20,20},Contours->{12}],
Graphics3D[{Red,PointSize[0.02],Point[{-2,-2,4}]}]
]

Show[
ContourPlot3D[x y+2z,{x,-3,-1},{y,-3,-1},{z,3,5},Contours->{12}],
ContourPlot3D[x+y+z==0,{x,-3,-1},{y,-3,-1},{z,3,5},Contours->{12}],
ContourPlot3D[x^2+y^2+z^2==24,{x,-3,-1},{y,-3,-1},{z,3,5},Contours->{12}],
Graphics3D[{Red,PointSize[0.04],Point[{-2,-2,4}]}]
]

Show[
ContourPlot3D[x y+2z,{x,-4,4},{y,-4,4},{z,-20,20},Contours->{-13}],
ContourPlot3D[x+y+z==0,{x,-4,4},{y,-4,4},{z,-20,20},Contours->{-13}],
ContourPlot3D[x^2+y^2+z^2==24,{x,-4,4},{y,-4,4},{z,-20,20},Contours->{-13}],
Graphics3D[{Red,PointSize[0.04],Point[{(1+3Sqrt[5])/2,(1-3Sqrt[5])/2,-1}]}]
]

{(1+3Sqrt[5])/2,(1-3Sqrt[5])/2,-1}//N

Show[
ContourPlot3D[x y+2z,{x,2,4},{y,-4,-2},{z,-2,0},Contours->{-13}],
ContourPlot3D[x+y+z==0,{x,2,4},{y,-4,-2},{z,-2,0},Contours->{-13}],
ContourPlot3D[x^2+y^2+z^2==24,{x,2,4},{y,-4,-2},{z,-2,0},Contours->{-13}],
Graphics3D[{Red,PointSize[0.04],Point[{(1+3Sqrt[5])/2,(1-3Sqrt[5])/2,-1}]}]
]