2014 AMC 12B Problems/Problem 11

Problem

Let be the parabola with equation and let . There are real numbers and such that the line through with slope does not intersect if and only if . What is ?

\[\textbf{(A)}\ 1\qquad\textbf{(B)}\ 26\qquad\textbf{(C)}\ 40\qquad\textbf{(D)}}\ 52\qquad\textbf{(E)}\ 80\] (Error compiling LaTeX. Unknown error_msg)

Solution

The line through only meets the parabola if the system of equations and $y -