p = IdentityMatrix[2]

p[[1, 1]] = 0.05;  p[[1, 2]] = 1 - p[[1, 1]]; 
    p[[2, 2]] = 0.05; 
    p[[2, 1]] = 1-p[[2, 
            2]]

(Subscript[π, 1]) = 
      p[[2, 1]]/(1 - p[[1, 1]] + p[[2, 1]])

(Subscript[π, 2]) = 1 - (Subscript[π, 1])

A[x_, y_] := 
      Table[p[[j, i]] If[i == 1, (x^2), (y^2)], {i, 2}, {j, 
          2}]

MatrixForm[A[x, y]]

f[y_] := Max[Eigenvalues[A[x, y]]]

f[y]

g[x_, y_] := 
      (1/2) (0.05` (x^2) + 0.05` (y^2) + 
            0.05` (Sqrt[1.` (x^4) + 1441.9999999999998` (x^2) (y^2) + 1.` (y^4)]))

Do[x = i/10; Print[x]; 
      Print[Solve[g[x, y] == 1, y]], {i, 0, 10}]

qqpts1 = {{0, 4.47213595499958`}, {0.1, 4.115905485564713`}, {0.2, 
          3.4065600189620464`}, {0.3, 2.75667129727528`}, {0.4, 
          2.2612832776668363`}, {0.5, 1.8949694168796212`}, {0.6, 
          1.6203914493719909`}, {0.7, 1.4095253494685003`}, {0.8, 
          1.2435135216772872`}, {0.9, 1.1098231017027762`}, {1, 
          1}}

Do[b = i/10; Print[b]; 
      Print[Solve[g[a, b] == 1, a]], {i, 10, 0, -1}]

qqpts2 = {{1, 1}, {1.1098231017027762`, 0.9}, {1.2435135216772872`, 
          0.8}, {1.4095253494685003`, 0.7}, {1.6203914493719909`, 
          0.6}, {1.6203914493719909`, 0.5}, {2.2612832776668363`, 
          0.4}, {2.75667129727528`, 0.3}, {3.4065600189620464`, 
          0.2}, {4.115905485564713`, 0.1}, {4.47213595499958`, 0}}

qqpts3 = qqpts1 . {{-1, 0}, {0, 1}}

qqpts4 = qqpts2 . {{-1, 0}, {0, 1}}

hh = ListPlot[Join[qqpts1, qqpts2, -qqpts2]]

<< Graphics`Spline`

hh2 = 
      Show[Graphics[{Thickness[ .006], Spline[qqpts1, Bezier]}]]

hh3 = 
      Show[Graphics[{Thickness[ .006], Spline[qqpts2, Bezier]}]]

hh4 = 
      Show[Graphics[{Thickness[ .006], 
            Spline[-qqpts1, Bezier]}]]

hh5 = 
      Show[Graphics[{Thickness[ .006], 
            Spline[-qqpts2, Bezier]}]]

hh6 = 
      Show[Graphics[{Thickness[ .006], Spline[qqpts3, Bezier]}]]

hh7 = 
      Show[Graphics[{Thickness[ .006], Spline[qqpts4, Bezier]}]]

hh8 = 
      Show[Graphics[{Thickness[ .006], 
            Spline[-qqpts3, Bezier]}]]

hh9 = 
      Show[Graphics[{Thickness[ .006], 
            Spline[-qqpts4, Bezier]}]]

f[x_] := (E^(-((Subscript[π, 1])/(Subscript[π, 2])) Log[Abs[x]]))

xmin = 0.2; xmax = 5;

g1 = 
      Plot[f[x], {x, xmin, xmax}, AxesOrigin -> {0, 0}, 
        AspectRatio -> 1, PlotRange -> All]

g2 = 
      Plot[f[x], {x, -xmin, -xmax}, AxesOrigin -> {0, 0}, 
        AspectRatio -> 1, PlotRange -> All]

g3 = 
      Plot[-f[x], {x, -xmin, -xmax}, AxesOrigin -> {0, 0}, 
        AspectRatio -> 1, PlotRange -> All]

g4 = 
      Plot[-f[x], {x, xmin, xmax}, AxesOrigin -> {0, 0}, 
        AspectRatio -> 1, PlotRange -> All]

l1 = 
      Graphics[{Dashing[{0.01, 0.01}], 
          Line[{{-1, 1}, {1, 1}}]}]

l2 = 
      Graphics[{Dashing[{0.01, 0.01}], 
          Line[{{-1, -1}, {1, -1}}]}]

l3 = 
      Graphics[{Dashing[{0.01, 0.01}], 
          Line[{{1, 1}, {1, -1}}]}]

l4 = 
      Graphics[{Dashing[{0.01, 0.01}], 
          Line[{{-1, 1}, {-1, -1}}]}]

Show[g1, g2, g3, g4, hh2, hh3, hh4, hh5, hh6, hh7, hh8, hh9, l1, l2, 
      l3, l4, AspectRatio -> 1]