2013 AMC 12B Problem 21

Consider the set of 30 parabolas defined as follows: all parabolas have as focus the point (0,0) and the directrix lines have the form y=ax+b with a and b integers such that a\in \{-2,-1,0,1,2\} and b\in \{-3,-2,-1,1,2,3\}. No three of these parabolas have a common point. How many points in the plane are on two of these parabolas?

\textbf{(A)}\ 720\qquad\textbf{(B)}\ 760\qquad\textbf{(C)}\ 810\qquad\textbf{(D)}\ 840\qquad\textbf{(E)}\ 870

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