Show[ContourPlot[x^2 + y^2 == 1, {x, -1.2, 1.2}, {y, -1.2, 1.2}],
Plot[x, {x, -1.2, 1.2}],
Graphics[{Dashed, Arrow[{{0, -1.2}, {0, 1.2}}]}],
Graphics[{Dashed, Arrow[{{-1.2, 0}, {1.2, 0}}]}],
Graphics[{Red, Line[{{Sqrt[2]/2, Sqrt[2]/2}, {Sqrt[2]/2, 0}}]}],
RegionPlot[
x <= Sqrt[2]/2 && y <= x && y >= 0, {x, -1.2, 1.2}, {y, -1.2, 1.2},
PlotStyle -> {Directive[Yellow, Opacity[0.6]]}, Mesh -> {5, 4}]]
Plot[Log[y + Sqrt[-1 + y^2]], {y, -10, 10}]