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在圆锥曲线这一块,利用标准方程来处理 一些相关的题目往往事半功倍,能大大简化运 算过程.因此,遇到此类题目时,大家很容易不 假思索地采用标准方程.殊不知,有时会产生 意想不到的错误. 请看以下两个例子: 1.点P与定点(2,0)的距离和它到直线x =8的距离的比是1/2,求点P的轨迹方程,并说 明轨迹是什么图形. 2.点P与定点(2,0)的距离和它到直线x =8的距离的比是2~(1/2)/2,求点P的轨迹方程,并 说明轨迹是什么图形. 题1为人教版新教材103页题,大部分同 学解答如下:
In the conic section, the use of standard equations to deal with some related topics tends to be more effective and can greatly simplify the calculation process. Therefore, when such problems are encountered, it is easy for people to adopt standard equations without thinking. As everyone knows, unexpected results are sometimes produced. Errors. Look at the following two examples: 1. The ratio of the distance between the point P and the fixed point (2,0) and its distance to the straight line x = 8 is 1/2. Find the trajectory equation of the point P and explain what the trajectory is. Graph. 2. The ratio of the distance between the point P and the fixed point (2,0) and its distance to the straight line x = 8 is 2~(1/2)/2. Find the trajectory equation of the point P and explain what the trace is. Question 1 is the 103 pages of the new teaching material of the People’s Education Press. Most of the students’ answers are as follows: