圆锥曲线切线的一种几何作法

• 作 者: 张留杰 白玉娟
• 机 构: 北京市陈经纶中学,北京市东方德才学校,
• 出 处: 中学生数学
• 发表日期: 2016年09期
• 关键词: 几何性质 全国高考 卷第 仿射变换

在平面几何学习的过程中,往往可以将圆中的一些典型问题推广到椭圆,进而再类比到双曲线和抛物线,充分体现了这些圆锥曲线的内在联系和统一性质.题目(2015年全国高考新课标卷第22题(1))如图1,AB为⊙O的直径,AC是⊙O的切线,BC交⊙O于点E.若D为AC的中点,证明:DE是⊙O的切线.由圆的几何性质不难证明直线DE与圆O相切于点E,再回首,发现此题蕴含着圆上任一点处的切线的一种作法,

In the process of plane geometry learning, some typical problems in the circle can often be generalized to ellipses and then to hyperbola and parabola, which fully reflects the intrinsic connection and unity of these conics. As shown in figure 1, AB is the diameter of ⊙O, AC is the tangent of ⊙O, BC is ⊙O at point E. If D is the midpoint of AC, it is proved that DE is ⊙O Of the tangent from the geometric nature of the circle is not difficult to prove that the line DE and the circle O tangent to the point E, and then look back and found that this question contains a tangent at any point on the circle of a practice,