题目
题型:不详难度:来源:
已知椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175706-70918.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-82455.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-46626.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-64005.gif)
(I)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-23794.gif)
(II)设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-23794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-34310.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-97937.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-44618.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-34310.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-97149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-73340.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-56839.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-66354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-23794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-42752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-42107.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-52500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-89245.gif)
答案
解:(I)方法1:椭圆的一个焦点是
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-59135.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175709-50380.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175709-65329.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175709-64627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175709-88161.gif)
方法2:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175709-65329.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175709-50160.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-46626.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175709-15957.gif)
∴椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175709-88161.gif)
(II)方法1:设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175709-47021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175710-90330.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175710-68792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175710-66257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175710-15796.jpg)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175710-60692.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175710-30046.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-56839.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175710-54830.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-66354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175710-31611.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175710-54830.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-12501.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-91456.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-85616.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-26295.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-25767.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175710-31611.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-12501.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-83553.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-60914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-22916.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-56894.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175712-17754.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175712-79270.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175712-89647.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-42752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-42107.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-89245.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-52500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-89245.gif)
方法2:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-97937.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-42752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-97149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-44618.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-42107.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-97149.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175707-97149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-56839.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-66354.gif)
显然
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-52500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-52500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175712-49861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175711-12501.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175712-31771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175713-78893.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175713-98996.gif)
直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-56839.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175713-72151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-66354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175713-44222.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175713-63624.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175714-60312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175714-84382.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175714-69581.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175714-97334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175714-74713.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175715-38374.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175715-63591.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175715-80509.gif)
∴直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-52500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175708-89245.gif)
解析
核心考点
试题【(本小题满分12分)已知椭圆经过点,一个焦点是.(I)求椭圆的方程;(II)设椭圆与轴的两个交点为、,不在轴上的动点在直线上运动,直线、分别与椭圆交于点、,证明】;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
已知椭圆G与双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175647-88734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175648-31225.gif)
(1)求椭圆G的方程
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175648-33070.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175648-12737.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175648-12737.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175648-29072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175648-22486.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175648-86097.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175640-68686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175640-32299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175640-12193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175641-59542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175641-55598.png)
(
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175641-52585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175642-64326.png)
①椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175640-68686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175641-59542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175642-92272.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175642-91220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175642-35619.png)
其中,所有正确结论的序号是( )
A.②③④ | B.①③④ | C.①②④ | D.①②③ |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175630-44553.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175630-33566.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175630-79018.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175631-28666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175631-97592.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175631-93087.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175631-41339.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175631-87684.gif)
(1)求此椭圆的方程;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175631-43931.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175624-54398.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175625-68507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175625-75647.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175614-69585.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175614-30354.gif)
(1)求椭圆C的标准方程;
(2)过椭圆C内一点M(2,1)引一条弦,使弦被点M平分,
求这条弦所在的直线方程。
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