1983 AHSME Problem 22

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 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

\textbf{(A)} \ 1 \qquad \textbf{(B)} \ \pi \qquad \textbf{(C)} \ 4 \qquad \textbf{(D)} \ 4 \pi \qquad \textbf{(E)} \ \text{infinite}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.