  In this paper, we prove the first incidence bound for points and conics over
prime fields. As applications, we prove new results on expansion of bivariate
polynomial images and on certain variations of distinct distances problems.
These include new lower bounds on the number of pinned algebraic distances as
well as improvements of results of Koh and Sun (2014) and Shparlinski (2006) on
the size of the distance set formed by two large subsets of finite dimensional
vector spaces over finite fields. We also prove a variant of Beck's theorem for
conics.
