21. Consider a set of 30 parabolas defined as follows: all parabolas have the focus at $(0,0)$, and the directrices are of the form $y=a x+b$, where $a \in\{-2,-1,0,1,2\}, b \in$ $\{-3,-2,-1,1,2,3\}$. It is known that no three parabolas have a common intersection point. Then, the number of intersection points between any two of these parabolas is ( ).
(A) 720
(B) 760
(C) 810
(D) 840
(E) 870
21. C.

In a set, any two parabolas intersect at most at two points. If two parabolas have the same orientation (the foci are on the same side of the directrices, and the directrices are parallel), in this case, the two parabolas do not intersect.
Thus, the number of intersection points is
$$
2 \mathrm{C}_{30}^{2}-2 \times 5 \times 2 \mathrm{C}_{3}^{2}=870-60=810 \text {. }
$$