  For a prime $p$ and an absolutely irreducible modulo $p$ polynomial $f(U,V)
\in \Z[U,V]$ we obtain an asymptotic formulas for the number of solutions to
the congruence $f(x,y) \equiv a \pmod p$ in positive integers $x \le X$, $y \le
Y$, with the additional condition $\gcd(x,y)=1$. Such solutions have a natural
interpretation as solutions which are visible from the origin. These formulas
are derived on average over $a$ for a fixed prime $p$, and also on average over
$p$ for a fixed integer $a$.
