圆锥曲线中的双参数问题

• 作 者: 华瑞芬
• 机 构: 安徽省灵璧县黄湾中学,
• 出 处: 高中数学教与学
• 发表日期: 2014年17期
• 关键词: 公共点 参数取值范围 抛物线方程 双参数 题设 韦达 数形结合 对称点 减函数 等量关系

如何求解圆锥曲线中的参数取值范围问题,对同学们来说已是难点,若是含有两个参数,可以说是难上加难了.对于后一种问题究竟该如何求解呢?下面举例分析,相信会对同学们有所启迪.例1若对任何a∈R,直线y=ax+1与椭圆(x~2)/5+(y~2)/m=1总有公共点,求m的取值范围.解由于直线y=ax+1(a∈R)恒过定点(0,1),若对任意x∈R,该直线与椭圆总有公共点,那么(0,1)应在椭圆上或其内部,所以0/5+1/m≤1.

How to solve the problem of the range of parameters in the conic is already difficult for the students. If it contains two parameters, it can be said that it is even harder to solve the problem. What is the solution to the latter problem? , I believe it will be enlightenment to students.Example 1 For any a ∈ R, the line y = ax +1 and the ellipse (x ~ 2) / 5 + (y ~ 2) / m = 1 there is always a common point, (0,1) for a straight line y = ax + 1 (a∈R), if there is always a common point between the line and the ellipse for any x∈R, then (0,1) Should be on the ellipse or inside, so 0/5 + 1 / m ≤ 1.