题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135714-19859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135714-40315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-14841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-52585.png)
(1)求椭圆的标准方程;
(2)设P是椭圆上异于A、B的任意一点,PQ⊥y轴,Q为垂足,M为线段PQ中点,直线AM交直线l于点C,N为线段BC的中点,求证:OM⊥MN.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-36403.png)
解析
试题分析:(1)根据椭圆的性质,建立方程,即可求得;(2)可以设点P坐标,然后用点P的坐标表示M、N的坐标,进而可以表示
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-50485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-56543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-82004.png)
试题解析:(1)依题意,得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-79603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-43639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-37430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135716-37849.png)
∴椭圆的标准方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-36403.png)
(2)证明:设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135716-31338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135716-40531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135716-64933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135716-29585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135716-77410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135717-72111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135717-38587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135717-72339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135717-21451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135717-28080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135717-96434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135714-40315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135717-64955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135718-44639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135718-20183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135718-28390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135718-10838.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135718-10150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135718-95009.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135719-37872.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135719-20009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-50485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135719-35325.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135719-42713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135719-62595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135719-61728.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135715-82004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135719-35325.png)
综上得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135719-35325.png)
核心考点
试题【如图,椭圆 (a>b>0)的上、下顶点分别为A、B,已知点B在直线l:上,且椭圆的离心率e =.(1)求椭圆的标准方程;(2)设P是椭圆上异于A、B】;主要考察你对椭圆的定义与方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135705-96755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135705-46144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135705-90177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135706-13692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135706-51764.png)
A.![]() | B.![]() | C.8 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135658-81656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135658-21173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135659-71837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135659-32259.png)
A.(0, 1) | B.(0,5) | C.[1,5) | D.[1,5)∪(5,+∞) |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135647-47165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135648-72325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135648-32218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135648-97345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135648-89699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135649-27513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135647-47165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135649-70740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135649-93116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135649-95912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135649-13581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135650-75500.jpg)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135647-47165.png)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135648-89699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135650-88081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135641-77325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135642-10455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135642-38479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135642-90735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135642-89829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135643-16283.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135630-70995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135630-28478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135630-45435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135631-17386.jpg)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135630-70995.png)
(2)如图,设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135630-70995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135631-42686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135631-99271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135631-42686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135631-28767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135632-85756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135632-61681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135632-33712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135632-40989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135632-40613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135633-30579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135632-33712.png)
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