题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210742-48038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210743-90559.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210743-69679.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210743-32585.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210743-10445.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-41747.gif)
(Ⅰ)求曲线C的方程;
(Ⅱ)证明不存在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-41747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-98494.gif)
(Ⅲ)过点P作
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210743-69679.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-22599.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210745-84126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210745-83063.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210745-13511.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210746-56585.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210746-90871.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210746-58853.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210747-88627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210747-10862.gif)
∴N1的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210747-76494.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210747-30545.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210748-56371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210748-65291.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210748-78667.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210749-12594.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210742-48038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210749-80322.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210749-59349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210745-13511.gif)
(2)证:点A(5,0)在曲线C即椭圆的外部,当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-41747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-41747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-41747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210750-13663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-41747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210750-75387.gif)
由方程组
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210750-17689.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210751-58124.gif)
依题意
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210751-14392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210751-74544.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210751-74544.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210752-36034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210752-52430.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210752-65104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210753-95714.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210753-75016.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-98494.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210753-65550.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-41747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210753-65550.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210754-37462.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210754-73510.gif)
但
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210754-78150.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-41747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210744-98494.gif)
(3)证明:由题有S
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210754-21588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210755-56574.gif)
则有方程组
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210755-81661.gif)
由(1)得:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210755-68174.gif)
将(2)、(5)代入(3)有
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210756-47445.gif)
整理并将(4)、(5)代入得
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210756-40515.gif)
易知
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210756-56801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210756-48307.gif)
因
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210757-17009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210757-77347.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210757-94679.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210757-72300.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210745-84126.gif)
核心考点
试题【在直角坐标平面上,O为原点,M为动点,,.过点M作MM1⊥轴于M1,过N作NN1⊥轴于点N1,.记点T的轨迹为曲线C,点A(5,0)、B(1,0),过点A作直线】;主要考察你对空间向量的直角坐标运算等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210732-20791.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210726-39412.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210726-30888.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210726-66802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210726-84439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210726-13274.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210726-74426.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210727-32026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210727-13258.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210727-27385.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210726-66802.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210717-33757.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210717-82803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210717-61787.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210717-25069.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210717-88343.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210717-72424.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210717-55590.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210718-90511.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210718-96377.gif)
A.以(![]() |
B.以(![]() |
C.以(![]() |
D.以(![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210706-81463.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210707-63776.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210707-63776.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210707-24705.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210707-17822.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210707-17822.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210706-81463.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210707-24705.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210707-63776.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105210707-17822.gif)
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