Consider the set of 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 $a\in -1,0,1$ and $b\in -2,-1,1,2$. No three of these parabolas have a common point. How many points in the plane are on two of these parabolas?