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
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![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](/uploads/image/z/5227827-51-7.jpg?t=%E8%BF%87%E6%8A%9B%E7%89%A9%E7%BA%BFy%5E2%3D2px+%E7%84%A6%E7%82%B9F%E7%9A%84%E5%BC%A6AB%2C%E7%82%B9A.B%E5%9C%A8%E5%87%86%E7%BA%BF%E4%B8%8A%E7%9A%84%E6%8A%95%E5%BD%B1%E4%B8%BAA1%2CB1%E6%B1%82%E8%A7%92A1FB1)
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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
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
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
∠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°.