Q:

Drawing two surfaces given implicitly by expressions containing one parameter

I have two curves and each one of them has two critical points which are saddles (i.e., I have four saddles). I try to draw them using Mathematica, but the saddles do not appear in the figure. (I need to draw them in the same plane). The first curve is given by 
x y + (b/2) y^2 - (3/2) x^2 y^2 + (1/4) y^4 + (1/2 b) x^2 - 
  (-2 + 22 b^2 + 3 b^4 - 7 Sqrt[3] b^3 Sqrt[4 + 3 b^2])/(72 b^2) = 0

with 0 < b < (1/Sqrt[6]). The second one is given by
x y + (b/2) y^2 - (3/2) x^2 y^2 + (1/4) y^4 + (1/2 b) x^2 - 
  (-2 + 22 b^2 + 3 b^4 + 7 Sqrt[3] b^3 Sqrt[4 + 3 b^2])/(72 b^2) = 0

with 0 < b < (1/Sqrt[6]).
Please help me to get the correct figure.

A:

It is not entirely clear what you are asking, but do you want something like this:
Manipulate[
 ContourPlot[{x y + (b/2) y^2 - (3/2) x^2 y^2 + (1/4) y^4 + (1/2 b) x^2 - 
         (-2 + 22 b^2 + 3 b^4 - 7 Sqrt[3] b^3 Sqrt[4 + 3 b^2])/(72 b^2) == 0, 
   x y + (b/2) y^2 - (3/2) x^2 y^2 + (1/4) y^4 + (1/2 b) x^2 - 
          (-2 +22 b^2 + 3 b^4 + 7 Sqrt[3] b^3 Sqrt[4 + 3 b^2])/(72 b^2) == 0},
         {x, -5, 5}, {y, -5, 5}], {b, 0.01, 1/Sqrt[6]}]

This gives you an interactive contour plot where you can change the value of $b$.

