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求圆锥曲线离心率的取值范围是解析几何的一类重要题型,是各类考试的命题热点.如何根据题设条件找到切入点,构造含离心率的不等式是解决这类问题的关键所在,也是学生普遍感到困惑之处,常用方法有:利用已知条件直接构造不等式;利用圆锥曲线的范围及最值构造不等式;数形结合借助平面几何知识构造不等式;利用判别式、均值不等式或其他基本不等式来构造不等式;利用函数的单调性构造不等式.
The range of conic curve eccentricity is an important kind of analytic geometry, which is the hot topic of all kinds of examinations.How to solve the problem of how to find the entry point according to the preconditions and construct the inequality with eccentricity , Which is also commonly confused by students. Common methods include: constructing inequalities directly using known conditions; constructing inequalities using the range and the maximum value of conic curves; constructing numerical inequalities by combining numerical knowledge with plane geometry; using discriminant, mean inequality, or other Basic inequalities to construct inequalities; Utilizing the monotonicity of functions to construct inequalities.