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题目1:过圆x~2+y~2=R~2上一点P(x_0,y_0)作圆的切线,切线方程为x_0x+y_0y=R~2。这是在高三复习解析几何的教学中,笔者先让学生做的人教A版《数学2》(必修)的一道课本例题。做完后,笔者提问:圆是椭圆的特殊情况,上述性质椭圆有吗?我们是不是可以用类比推理的思想去考虑一下?在这样引导下,通过类比学生轻松得到以下三个类似的结论:
Problem 1: Rounding x ~ 2 + y ~ 2 = R ~ 2 The previous point P (x_0, y_0) is a tangent to the circle, and the tangent equation is x_0x + y_0y = R ~ 2. This is the third year of reviewing analytical geometry teaching, the author let the students to teach people to teach A version of “Mathematics 2” (compulsory) a textbook example. After done, I asked the question: the circle is a special case of oval, the above properties oval there? We can not use analogical reasoning to think about it? Under this guidance, through analogy students easily get the following three similar conclusions: