`Consider\ the\ two \ functions\ f(x)=x^(2)+2bx+1 and g(x)=2a(x+b)` where the variable x and the constants a and b are real numbers.Each such pair of the constants a and b may be considered as a point (a, b) in an ab - plane.Let S be the set of such points (a b) for which the graphs of y=f(x) and y=g(x) do not intersect (in the xy - plane). The area of S is