题目
题型:不详难度:来源:
已知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005036-22759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005036-37744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005036-68438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005036-45544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005037-21901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005037-15787.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005037-80076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-13886.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-81005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-30486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-44603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-13886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-28853.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-37972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-13886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-40910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-39308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005037-80076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005040-39737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-39308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005037-21901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-13886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005040-59886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005040-99768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005040-67099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005041-12142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-13886.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005041-24412.png)
解析
试题分析:(1)证明:设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-37972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-13886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-40910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-39308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005037-80076.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005041-67753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005041-58627.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005040-39737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-39308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005037-21901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-13886.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005040-59886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005040-99768.png)
∴两式相减得:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005042-26938.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005040-67099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005041-12142.png)
∴曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-13886.png)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-37972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-13886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-40910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-39308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005042-36218.png)
∴曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-13886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005042-30841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-39308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-81005.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005042-90387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005043-75571.png)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005043-72240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005043-84072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005044-39774.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005044-84999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005044-21817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-39308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005037-21901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-37972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005044-98213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005044-30544.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-39308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005043-75571.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005045-33719.png)
∴2
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005045-14000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005045-10620.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005045-37605.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005045-85005.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005046-31107.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005046-72208.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005046-13859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005039-39308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005038-44603.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005047-59080.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005047-13118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005041-24412.png)
点评:直线与椭圆相交时,常联立方程利用韦达定理求解关于弦长,中点弦及垂直夹角等问题;求椭圆离心率的题目需要转化出关于
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005047-43168.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005029-24346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005029-93030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005030-11426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005030-22975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005029-93030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005030-22975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005030-69564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005020-76282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005020-33649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005020-43701.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005020-72296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005020-35124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005021-24490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005021-15181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005000-84967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005001-93361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005001-75305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005001-91593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005001-88064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005002-95013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005002-77441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005002-94281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005002-30883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005003-43018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005003-66776.png)
(Ⅰ)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005001-91593.png)
(Ⅱ)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005003-26872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005003-54941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005001-91593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005004-45897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005004-74854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005004-71575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005001-91593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005004-20966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005005-44338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026005005-98183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004954-63444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004954-79165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004939-70034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004939-43042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004939-36508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004939-53850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004940-76370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004939-36508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004940-24375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004940-20848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004940-73077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004940-70616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004941-73873.jpg)
(I)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004939-36508.png)
(Ⅱ)求线段MN的长度的最小值;
(Ⅲ)当线段MN的长度最小时,在椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004939-36508.png)
样的点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004941-29464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004941-56257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004941-85960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004941-29464.png)
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