Plot3D[y^4+x^2y^2+x,{x,-1.2,1.2},{y,-1.2,1.2},BoxRatios->{1,1,1},Mesh->None,PlotStyle->Opacity[0.7]];
ParametricPlot3D[{{((-1-(Sqrt[1+4 (y^2)-4 (y^6)]))/(2 (y^2))),y,1},{((-1+(Sqrt[1+4 (y^2)-4 (y^6)]))/(2 (y^2))),y,1}},{y,-1.2,1.2},PlotStyle->Red,PlotStyle->Thickness[.5]];
Graphics3D[Arrow[{{0,1,1},{0,1,1}+ 1/20{1,4,17}}]];
Show[%%%,%%,%]

ContourPlot[y^4+x^2y^2+x,{x,-1.5,1.5},{y,-1.5,1.5},Contours->20]
Graphics[ContourPlot[y^4+x^2y^2+x==1,{x,-1.5,1.5},{y,-1.5,1.5},ContourStyle->Red]];
Graphics[Arrow[{{0,1},{1/12,1+1/3}}]];
Show[%%%,%%,%]

Plot3D[Sin[√(x^2+y^2)],{x,-3Pi,3Pi},{y,-3Pi,3Pi}]

Plot3D[Sin[√(x^2+y^2)],{x,-6Pi,6Pi},{y,-6Pi,6Pi}]