AMC 10B 2016 Problem 9

All three vertices of \triangle A B C lie on the parabola defined by y=x^{2}, with A at the origin and \overline{B C} parallel to the x-axis. The area of the triangle is 64 . What is the length B C ?

Answer Choices
A. 4
B. 6
C. 8
D. 10
E. 16