AMC 12 2008b Problem 17

Let $A$, $B$ and $C$ be three distinct points on the graph of $y=x^2$ such that line $AB$ is parallel to the $x$-axis and $\triangle ABC$ is a right triangle with area $2008$. What is the sum of the digits of the $y$-coordinate of $C$?

(Solution)

\textbf{(A)}\ 16 \textbf{(B)}\ 17 \textbf{(C)}\ 18 \textbf{(D)}\ 19 \textbf{(E)}\ 20