2014 AMC 12B 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\qquad\textbf{(B)}\ 26\qquad\textbf{(C)}\ 40\qquad\textbf{(D)}\ 52\qquad\textbf{(E)}\ 80

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.