Problem 92

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Problem 92: (2008 AmC12B, 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 $C$? $\textbf{(A)}\ 16\qquad$ $\textbf{(B)}\ 17\qquad$ $\textbf{(C)}\ 18\qquad$ $\textbf{(D)}\ 19\qquad$ $\textbf{(E)}\ 20$

Solution

Exercise 92: Solution

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 (right angle at $C$) with area $100$. What is the sum of the digits of the $y$-coordinate of $C$?

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