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解析几何中确定参数的取值范围是一类较为常见的探索性问题,我们在教学中发现不少学生对处理这类问题无从下手,不知道确定参数范围的不等式从何而来,其根本原因是学生对这类问题的背景不清楚。本文通过一些实例介绍这类问题形成的几个背景及相应的解法。背景之一:题目所给条件这是求范围问题最显然的一个背景。例1 已知P是椭圆x~2/45+y~2/20=1上在第一象限内的一点,且它与椭圆两个焦点的连线互相垂直,若点P
Determining the range of parameters in analytical geometry is a relatively common exploratory problem. We found in teaching that many students have no way to deal with such problems, and do not know where to determine the inequalities of the parameters, and its root causes. It is the students’ background to this type of question that is not clear. This article introduces some backgrounds and corresponding solutions to these problems through some examples. One of the backgrounds: the conditions given by the topic This is the most obvious context for the scope problem. Example 1 It is known that P is a point in the first quadrant of the ellipse x~2/45+y~2/20=1, and it is perpendicular to the line connecting the two focuses of the ellipse, if the point P