令x = 0 ,得到点C坐标:C(0 ,6)
又y = (1/4)x^2 - (5/2)x + 6 = (1/4)(x - 4)(x - 6) ,且A在B左侧 ,
∴A(4 ,0) ,B(6 ,0)
∵P在AC之间 ,∴P(x ,y)在第一象限中 ,∴0 < x < 4 ,0 < y < 6 ,
∴S = (1/2)·4·y = (1/2)x^2 - 5x + 12 ,0 < x < 4
存在使得PO = PA的点P ,此时P即为OA的中垂线与抛物线的交点 ,易得OA中垂线为:x = 2 ,联立抛物线方程得:y = (1/4)·4 - (5/2)·2 + 6 = 2 ,
即:使得PO = PA的P点坐标为:P(2 ,2)