# How to plot a lines in 3d representation as a function of one parameter

I have two functions and I am not sure how to set them to be 3 axes -> x, y and β and to plot lines for different values of β. It is important for example to set β {0,2}, and I am looking for lines in 3D for different β {0.25,0.5,0.75,...1.75}

 x = 1/2 Sqrt[2 + β^4 + 1/β^4];
y = Sqrt[1/2 (β^2 + 1/(β^2) ) - 1/2 Sqrt[2 + β^4 + 1/β^4]];

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FullSimplify[ Sqrt[1/2 (\[Beta]^2 + 1/(\[Beta]^2)) - 1/2 Sqrt[2 + \[Beta]^4 + 1/\[Beta]^4]], Assumptions -> {\[Beta] > 0 }] -> 0 –  esprit Feb 26 at 1:57

I don't really understand the question and the 3D part since your y[x] is equal to 0 (as esprit implied) but here might be a way to go:
x[β_] := 1/2 Sqrt[2 + β^4 + 1/β^4];