A Cannon Fires a Cannonball as Shown in the Figure $( x - 1200 ) ^ { 2 } = - \frac { 400 } { 3 } ( y - 800 )$

Multiple Choice

A cannon fires a cannonball as shown in the figure. The path of the cannonball is a parabola with vertex at the highest point of the path. If the cannonball lands 1600 ft from the cannon and the highest point it reaches is 2400 ft above the ground, find an equation for the path of the cannonball. Place the origin at the location of the cannon.

A) $( x - 1200 ) ^ { 2 } = - \frac { 400 } { 3 } ( y - 800 )$
B) $( x - 800 ) ^ { 2 } = - \frac { 400 } { 3 } ( y - 2400 )$
C) $( x - 800 ) ^ { 2 } = - \frac { 800 } { 3 } ( y - 2400 )$
D) $( x - 2400 ) ^ { 2 } = - \frac { 800 } { 3 } ( y - 800 )$
E) none of these