题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233542-97979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-81628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-81628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-81881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-87766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-23241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233544-29784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233544-99007.png)
(Ⅰ)求该椭圆的离心率;
(Ⅱ)设线段
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-23241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233544-49302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-23241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233545-29846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233545-29862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233545-94682.png)
记△
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233546-58884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233546-81957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233546-23006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233546-44692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233547-29113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233547-37593.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233547-84136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233547-37593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233547-36482.png)
解析
试题分析:(Ⅰ)解:依题意,当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-23241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233548-59609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233544-29784.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233548-30985.png)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233548-21731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233548-76517.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233549-13332.png)
所以椭圆的离心率为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233547-84136.png)
(Ⅱ)解:由(Ⅰ),椭圆的方程可设为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233549-44536.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233549-54729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233550-73869.png)
依题意,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-23241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233550-36779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-23241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233550-94986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233550-59480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233551-23072.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233551-92965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233551-41108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233551-94954.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233552-80731.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233552-54349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233552-24738.png)
因为 △
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233546-58884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233546-23006.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233553-79739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233553-93652.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233547-37593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233547-36482.png)
点评:中档题,求椭圆的标准方程,主要运用了椭圆的几何性质,a,b,c,e的关系。曲线关系问题,往往通过联立方程组,得到一元二次方程,运用韦达定理。对于三角形面积计算问题,注意应用已有垂直关系及弦长公式。本题应用韦达定理,简化了解题过程。
核心考点
试题【如图,椭圆的左焦点为,过点的直线交椭圆于,两点.当直线经过椭圆的一个顶点时,其倾斜角恰为.(Ⅰ)求该椭圆的离心率;(Ⅱ)设线段的中点为,的中垂线与轴和轴分别交于】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233538-92893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233539-46391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233539-98110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233539-68233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233534-65965.png)
A.(0,2) | B.(0,-2) | C.(4,0) | D.(-4,0) |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233527-47879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233527-13784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-95588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-89786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-95588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233517-41613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233517-47902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-95588.png)
(1)写出抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-95588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233502-16498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233503-75302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233503-73218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233503-70222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233504-21374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233504-46257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233504-52481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-84608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233502-16498.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233502-16498.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233504-52481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-72435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-43499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-66258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233503-70222.png)
(3)试问
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-43499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-84608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233504-52481.png)
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