Chandan,
It is helpful if you use the "<>" code-editing in your posts.
This may be helpful.
Create a list of plots
plots = Table[
With[{aParam = 2 Sqrt[(wParam - 1)]},
ContourPlot[
1/(1 - y^2)^0.5 + w^2/2 == wParam, {w, -aParam, aParam}, {y, -1,
1}]],
{wParam, 1.0001, 1.5, .1}
]
Show all of the plots together:
Show[plots, PlotRange -> All]
Note, W=1 gives a plot range of {0,0}....
