  Consider the hypergraph whose vertex set is a family of $n$ lines in general
position in the plane, and whose hyperedges are induced by intersections with a
family of pseudo-discs. We prove that the number of $t$-hyperedges is bounded
by $O_t(n^2)$ and that the total number of hyperedges is bounded by $O(n^3)$.
Both bounds are tight.
