AMC 12 2014b Problem 17

Let $P$ be the parabola with equation $y=x^2$ and let $Q = (20, 14)$. There are real numbers $r$ and $s$ such that the line through $Q$ with slope $m$ does not intersect $P$ if and only if $r < m < s$. What is $r + s$?

\textbf{(A)}\ 1 \textbf{(B)}\ 26 \textbf{(C)}\ 40 \textbf{(D)}\ 52 \textbf{(E)}\ 80