受2007年湖南高考卷理科20题第(2)问的设问方式的启发,我们设置了下面这道探索性问题.题已知A,B,C是焦点为F的抛物线y2=2px(p0)上的顺次三点,且都在x轴的同一侧,若BF⊥x轴,试问在直线AC上是否存在定点P,使得BF总是平分∠AFC若存在,请求出点P的坐标;若不存在,请说明理由.思路分 Inspired by the questioning style of Question 2 (2) of the 20 questions in the 2007 Hunan College Entrance Examination, we set out the following exploratory question. Known A, B, and C are parabolic y2=2px with focus F (p0 Three points in sequence, and all on the same side of the x-axis, if BF ⊥ x-axis, ask if there is a fixed point P on the straight line AC, so that BF always bisection ∠ AFC if there is a request for the coordinates of the point P; If not, please explain the reason.