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虽然高中教材平面解析几何部分历经变迁,尤其是近十年,从新课程教材到新课标教材,但圆锥曲线光学性质一直具有一席之地[1]～[6],高中物理教材中也有所涉及。同时数学教学内容与生产实践相结合的要求早已深入人心,加之“导数”内容正式加盟考试要求,相关例、习题也出现在各种版本正式数学教材中[2]～[6],甚至高考模拟试题及正式试题中都有所涉及[7]。我们先看以下事实:【定理1】从椭圆的一个焦点发出的光线或声波在经过椭圆周上反射后,反射线都经过椭圆的另一个焦点.
Although the geometry of high school textbooks has undergone changes in the plane analysis, especially in recent ten years, from the new curriculum materials to the new curriculum materials, the optical properties of the conic have always had a place [1] ~ [6], high school physics textbooks are also involved. At the same time, the requirement of combining mathematics teaching content and production practice has already been deeply rooted in the hearts of people. In addition, the requirements of the “derivative” content officially join the exam, and related examples and exercises also appear in various versions of formal mathematics textbooks [2] ~ [6] Entrance exam simulation questions and formal questions are involved [7]. Let us first look at the following fact: Theorem 1: A ray or sound wave emitted from one focal point of an ellipse is reflected by the elliptical circumference, and the reflected ray passes through the other focal point of the ellipse.