2024年数学高考大一轮复习第九章 §9.12　圆锥曲线中范围与最值问题

这是一份2024年数学高考大一轮复习第九章 §9.12　圆锥曲线中范围与最值问题，共4页。
§9.12　圆锥曲线中范围与最值问题题型一　范围问题例1 (2023·淄博模拟)已知F(，0)是椭圆C：＋＝1(a>b>0)的一个焦点，点M在椭圆C上．(1)求椭圆C的方程；(2)若直线l与椭圆C相交于A，B两点，且kOA＋kOB＝－(O为坐标原点)，求直线l的斜率的取值范围．________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________思维升华 圆锥曲线中取值范围问题的五种常用解法(1)利用圆锥曲线的几何性质或判别式构造不等关系，从而确定参数的取值范围．(2)利用已知参数的范围，求新参数的范围，解决这类问题的核心是建立两个参数之间的等量关系．(3)利用隐含的不等关系建立不等式，从而求出参数的取值范围．(4)利用已知的不等关系构造不等式，从而求出参数的取值范围．(5)利用求函数值域的方法将待求量表示为其他变量的函数，求其值域，从而确定参数的取值范围．跟踪训练1 (2022·济宁模拟)已知抛物线E：y2＝2px(p>0)上一点C(1，y0)到其焦点F的距离为2.(1)求实数p的值；(2)若过焦点F的动直线l与抛物线交于A，B两点，过A，B分别作抛物线的切线l1，l2，且l1，l2的交点为Q，l1，l2与y轴的交点分别为M，N.求△QMN面积的取值范围．________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________题型二　最值问题例2 (2022·苏州模拟)已知双曲线C：－＝1(a>0，b>0)过点(2，1)，渐近线方程为y＝±x，直线l是双曲线C右支的一条切线，且与C的渐近线交于A，B两点．(1)求双曲线C的方程；(2)设点A，B的中点为M，求点M到y轴的距离的最小值．________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________思维升华 圆锥曲线中最值的求法(1)几何法：若题目的条件和结论能明显体现几何特征及意义，则考虑利用图形性质来解决．(2)代数法：若题目的条件和结论能体现一种明确的函数，则可首先建立目标函数，再求这个函数的最值，求函数最值的常用方法有配方法、判别式法、基本不等式法及函数的单调性法等. 跟踪训练2 (2023·临沂模拟)已知椭圆C：＋＝1(a>0，b>0)的左、右焦点分别为F1，F2，离心率为，直线x＝被C截得的线段长为.(1)求C的方程；(2)若A和B为椭圆C上在x轴同侧的两点，且＝λ，求四边形ABF1F2面积的最大值．________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________