(*Intersection of Two Cylinders*)

Manipulate[
Show[
ContourPlot3D[x^2==z,{x,-3,3},{y,-3,3},{z,-1,6},BoundaryStyle->None,ContourStyle->{Blue,Opacity[opP]},Mesh->None,Axes->False,ImageSize->600],
 ContourPlot3D[x^2+y^2==4,{x,-2,2},{y,-2,2},{z,-1,6},BoundaryStyle->None,ContourStyle->{Green,Opacity[opC]},Mesh->None],
ParametricPlot3D[{2*Cos[t],2*Sin[t],4*Cos[t]^2}, {t, 0, 2*Pi}, PlotStyle->{Opacity[opI],Thick,Red}]
],
{{opC,1,Text[Style["Circular Cyl. Opacity",RGBColor[0,0.5,0]]]},0,1},
{{opP,1,Text[Style["Parabolic Cyl. Opacity", RGBColor[0,0,0.5]]]},0,1},
{{opI,0,Text[Style["Intersection Opacity",RGBColor[0.5,0,0]]]},0,1},
ControlPlacement->Top
]