2018 AMC 12A Problem 16

Which of the following describes the set of values of a for which the curves x^2+y^2=a^2 and y=x^2-a in the real xy-plane intersect at exactly 3 points?

\textbf{(A) }a=\frac14 \qquad \textbf{(B) }\frac14 < a < \frac12 \qquad \textbf{(C) }a>\frac14 \qquad \textbf{(D) }a=\frac12 \qquad \textbf{(E) }a>\frac12 \qquad

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