题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234046-78466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234046-38234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234046-15833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234046-70016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-74795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-80202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-35179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
(1)求椭圆标准方程;
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234048-74844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234048-13744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234048-10519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234048-50257.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234049-41323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234048-13744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234049-35800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234049-20932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234049-83445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-80202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234050-87877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234049-20932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234049-83445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234050-89553.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234050-38460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234050-11483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234050-50616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234051-51862.png)
解析
试题分析:(1)根据题意由已知可得:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234051-63684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234050-38460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234048-74844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234048-13744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234051-42612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234051-51776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234052-51173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234052-23222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234052-64329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234052-90874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234053-79657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234053-16990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234053-69341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234053-17891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234054-22824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234054-39358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234054-82686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234054-93026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234055-64537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234055-37463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234055-67870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234054-93026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234055-68282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234056-37983.png)
(I)由题设可知:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234051-63684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234056-18127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234056-99605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234056-63783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234056-29060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234050-38460.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234057-83051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234057-51660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234057-18613.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234057-21512.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234052-51173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234052-23222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234058-53144.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234058-59229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234058-63374.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234052-90874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234053-79657.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234059-16828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234053-16990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234059-91841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234059-15151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234059-58001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234059-15064.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234053-69341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234053-17891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234100-69481.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234054-39358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234054-82686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234054-93026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234055-64537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234047-54777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234055-37463.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234055-67870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234054-93026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234055-68282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234055-68282.png)
设该椭圆的左、右焦点为
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234056-37983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234050-87877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234100-48876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234100-84721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234051-51862.png)
核心考点
试题【已知椭圆的右准线,离心率,,是椭圆上的两动点,动点满足,(其中为常数).(1)求椭圆标准方程;(2)当且直线与斜率均存在时,求的最小值;(3)若是线段的中点,且】;主要考察你对均值不等式等知识点的理解。[详细]
举一反三
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234031-39109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234031-84197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234031-71754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234031-79748.png)
解法如下:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234031-82722.png)
当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234032-74728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234032-92073.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234031-79748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234032-88429.png)
应用上述解法,求解下列问题:
(1)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234032-51997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234033-40542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234033-12272.png)
(2)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234033-20446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234033-87442.png)
(3)已知正数
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234033-64091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234034-56946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234034-46323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234034-31067.png)
求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234034-25594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234021-74335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234021-53526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234022-11484.png)
(1)求抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234022-57332.png)
(2)当圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234021-53526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234022-88242.png)
(3)当圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234021-53526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234022-72692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234023-19974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234023-84863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234003-81201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234004-86060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234004-80508.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234004-54061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234004-35950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234005-35281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015234005-61677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015233956-78860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015233956-37379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015233952-91298.png)
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