过抛物线y^2=2px 焦点F的弦AB,点A.B在准线上的投影为A1,B1求角A1FB1
问题描述：
过抛物线y^2=2px 焦点F的弦AB,点A.B在准线上的投影为A1,B1求角A1FB1
答
∠A1FB1=90度.由抛物线的定义,知|AA1|＝|AF|,|BB1|=|BF|,
∴∠AA1F＝∠AFA1,∠BB1F＝∠BFB1.设x轴交准线于点K.∵A1A‖B1B‖x轴,
∴∠AA1F＝∠A1FK,∠BB1F＝∠B1FK,
∴∠A1FB1＝∠A1FK+∠B1FK＝(∠AFA1+∠A1FK+∠B1FK+∠BFB1)/2=180°/2=90°.