## Location of the third point on the parabola for largest triangle

**Problem**

The line *y* = 2*x* + 8 intersects the parabola *y* = *x*^{2} at points *A* and *B*. Point *C* is on the parabolic arc *AOB* where *O* is the origin. Locate *C* to maximize the area of the triangle *ABC*.

A. (1.1, 1.21)

B. (1, 1)

C. (0.9, 0.81)

D. (1.2, 1.44)