BY-MO 2001 Problem 1

On the Cartesian coordinate plane, the graph of the parabola $y = x^2$ is drawn. Three distinct points $A$ , $B$ , and $C$ are marked on the graph with $A$ lying between $B$ and $C$ . Point $N$ is marked on $BC$ so that $AN$ is parallel to the y-axis. Let $K_1$ and $K_2$ are the areas of triangles $ABN$ and $ACN$ , respectively. Express $AN$ in terms of $K_1$ and $K_2$ .