求离心率的取值范围是解析几何中的一类典型问题.这类问题的求解过程中往往涉及多个知识点,综合性强,方法也多种多样.解这类问题的关键是构造不等式.现给出一些破解圆锥曲线离心率取值范围问题的常见策略.一、直接应用已知条件构造函数关系例1设a>1,则双曲线x~2/a~2-y~2/((a+1)~2)=1的离心率e的取值范围是().A.(2~(1/2),2) B.(2~(1/2),5~(1/2))C.(2,5) D.(2,5~(1/2)) The range of seeking the eccentricity rate is a typical problem in analytic geometry.There are many knowledge points in the solving process of these kinds of problems, which are comprehensive, and the methods are also varied.The key to solve this kind of problem is to construct the inequality Now, some common strategies for solving the range of conic curve eccentricity are given. First, the direct application of the known conditions Constructor relations Example 1 Suppose a> 1, the hyperbola x ~ 2 / a ~ 2-y ~ 2 / (2) (1/2), 2) B. (2 ~ (1/2), 5 ~ (1/2) 1/2)) C. (2,5) D. (2,5 ~ (1/2))