2015 AMC 12A Problem 12

The parabolas y=ax^2 - 2 and y=4 - bx^2 intersect the coordinate axes in exactly four points, and these four points are the vertices of a kite of area 12. What is a+b?

\textbf{(A)}\ 1\qquad\textbf{(B)}\ 1.5\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 2.5\qquad\textbf{(E)}\ 3

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