题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-40193.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-72555.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-96865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-10695.gif)
(Ⅰ)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-96650.gif)
(Ⅱ)设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-96650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-30021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-70081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-40426.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-23280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-40319.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-54200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-41361.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-96650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-55645.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-14984.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-23280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-40319.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-77351.gif)
答案
解:(I)方法1:椭圆的一个焦点是
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-26245.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-51767.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-78020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40318.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-91938.gif)
方法2:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-78020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-63265.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-96865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-50066.gif)
∴椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-91938.gif)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-86345.jpg)
方法1:当点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-23280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-30021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-55645.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-14984.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-70081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-40426.gif)
若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-77351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-77351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-30021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-35018.gif)
当点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-23280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-30021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-60916.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-78751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-63459.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-43541.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-60152.gif)
直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-54200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-44212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-41361.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-73735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-44212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-32708.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-41078.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-74431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-29358.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-61100.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-73735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-32708.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-44513.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175729-59784.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175729-74380.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175729-74832.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175729-13985.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175729-15741.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175729-30478.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175729-18970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-46349.gif)
∴当点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-23280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-40319.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-97829.gif)
方法2:直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-97829.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-30021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-97829.gif)
当点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-23280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-30021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-60916.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-78751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-63459.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-43541.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175727-60152.gif)
直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-54200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-44212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-41361.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-73735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-44212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-32708.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-41078.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-74431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-29358.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-35215.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-73735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-32708.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-44513.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175729-59784.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175729-74380.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-88117.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-75849.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-97829.gif)
方法3:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-70081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-55645.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-23280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-40426.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-14984.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-23280.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-23280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-54200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-41361.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175731-65534.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175728-32708.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175731-80056.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175731-39115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175731-15600.gif)
直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-54200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175732-66401.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-41361.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175732-64133.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175732-66517.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175732-45153.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175732-27593.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175733-10059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175733-95306.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175733-61805.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175733-73794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175734-28014.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-46349.gif)
∴直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175731-65534.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-97829.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175724-30021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-97829.gif)
∴当点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-23280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175725-40319.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175726-40608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175730-97829.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、,点在直线上,直线、分别与椭圆交于、两点.试问:当点在直线上运】;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
![](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)
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)
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- 1下列加点字的读音全都正确的一组是( )A.悲怆(chuànɡ)浣洗(huàn)赍钱(zī)夙兴夜寐(sù)B.咎言(
- 2近地面大气的热量主要直接来自( )A.①太阳辐射B.②大气辐射C.③地面辐射D.④大气逆辐射
- 32006年10月11日,国务院总理温家宝签署第476号国务院令,公布了《长城保护条例》,长城的保护由此走上了法制化轨道。
- 4目前,我们可以通过电视等各种媒体及时了解全国各地的空气质量状况.现计入空气污染指数的项目为( )A.二氧化硫、二氧化氮
- 5以下方法不能用来区别一氧化碳、二氧化碳两种无色气体的是①通入澄清的石灰水中;②通入紫色石蕊试液中;③闻气味,是否有刺激性
- 6将电阻为1欧姆的均匀铜棒拉成半径为原来的13的铜线,则这时铜线的电阻为( )A.3ΩB.81ΩC.9ΩD.18Ω
- 7(1)在“探究求合力的方法”的实验中,要求每次合力与分力产生相同的效果,必须______A.每次将橡皮条拉到同样的位置B
- 8不同的材料具有不同的性能,将下列材料具有的性能用短线连起来:材料种类--------相应的性能①钢化玻璃-----A.耐
- 9小张(已年满18周岁)的下列行为中,属于参加政治生活的是 [ ]①投票选举
- 10学校打算为校刊征集新的栏目,请你设想一个栏目,并作简要说明。栏目:____________________ 简要说明:_