题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135333-20498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135334-73831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135334-35143.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135333-20498.png)
(2)若椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135333-20498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135334-24644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135334-24644.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135335-16754.png)
解析
试题分析:本题主要考查椭圆的标准方程及其几何性质、韦达定理等基础知识,考查学生的分析问题解决问题的能力、转化能力和计算能力.第一问,根据椭圆的标准方程应满足的条件得:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135335-38116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135335-57594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135335-15062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135336-67579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135336-55450.png)
试题解析:(1)根据已知条件有
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135335-38116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135335-57594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135333-20498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135336-12425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135336-79455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135336-81533.png)
由于椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135333-20498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135337-79448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135335-16754.png)
(2)设交点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135334-24644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135337-23449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135334-24644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135337-28270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135335-16754.png)
(1)当斜率不存在或等于零时,易得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135334-24644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135334-24644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135337-39902.png)
(2)当斜率存在且非零时,则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135338-71432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135338-70979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135337-28270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135338-56028.png)
与椭圆方程联立消
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135336-12425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135338-42342.png)
由相切,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135339-30551.png)
化简整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135339-70213.png)
因过椭圆外一点有两条直线与椭圆相切,由已知两切线垂直,故
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135339-12916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135339-65642.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135340-22660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135340-37329.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135337-39902.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135334-24644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135340-31502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135334-24644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135340-31502.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135320-55840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135320-31674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135321-78015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135321-52820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135321-74653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135320-31674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135321-17072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135322-28484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135322-41501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135322-17918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135322-44354.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135322-13188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135320-31674.png)
(2)设动点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135323-29706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135323-50078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135320-31674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135323-84582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135323-78161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135324-92830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135307-55591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135308-37175.jpg)
(1)求椭圆E的方程;
(2)在椭圆E上是否存点Q,使得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135308-17327.png)
(3)过椭圆E上异于其顶点的任一点P,作
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135308-21704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135308-90817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135253-15619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135253-70658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135253-23965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-74664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-26825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-67188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-86077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-55471.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-26825.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135255-98752.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-86077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135255-71571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135255-34788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135255-76047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135240-35591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135241-19554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135241-36775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135241-43450.png)
(1)求椭圆的方程;
(2)若C、D分别是椭圆长轴的左、右端点,动点M满足
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135241-62816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135242-44072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135242-28641.png)
(3)在(2)的条件下,试问
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135242-43783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-28180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-62454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-89355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-16386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-14039.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-28180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-16386.png)
(2)过点F的直线交抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-16386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-25925.png)
(3)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-52113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-28180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135224-18646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135224-25241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-28180.png)
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