题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200223-39620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-23516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-90547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-97314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-67949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-78039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-81079.png)
(Ⅰ)当⊙
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-36850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-34073.png)
(Ⅱ)当⊙
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-92137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
(Ⅲ)求证:⊙
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200225-75040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200225-68832.png)
M
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200225-76310.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200225-86210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200225-44834.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200225-68197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200226-13600.png)
又⊙
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200226-51560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200226-25384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200226-97051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200226-80100.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-34073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200225-75040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200225-68832.png)
(Ⅱ)因为直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200226-49911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200226-22696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200226-68332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200226-49911.png)
距离为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200227-53123.png)
化简,得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200227-59839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200227-89235.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200227-84805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200227-51889.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200227-84805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200227-65109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200228-24425.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200227-51889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200228-65405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200225-76310.png)
(Ⅲ)⊙
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200228-55657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200228-21740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200229-33355.png)
证明:因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200229-94009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200229-89779.png)
又⊙
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200229-14435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200230-30860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200230-23852.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200230-96573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200229-33355.png)
(说明:结合椭圆定义用几何方法证明亦可)
核心考点
试题【(本小题满分16分)已知椭圆:的左、右焦点分别为,下顶点为,点是椭圆上任一点,⊙是以为直径的圆.(Ⅰ)当⊙的面积为时,求所在直线的方程;(Ⅱ)当⊙与直线相切时,】;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/20191023/20191023200207-27260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200207-73638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200207-12934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200208-89410.gif)
(Ⅰ)求动圆圆心的轨迹C;
(Ⅱ)若轨迹C与直线y="kx+m" (k≠0)相交于不同的两点M、N,当点A(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200208-75942.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200208-73263.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200209-99432.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200202-18351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200202-98542.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200202-36378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200203-89648.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200203-60620.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200203-67210.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200204-23740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200148-12735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200148-69881.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200148-50112.gif)
(1)求椭圆的方程;
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200149-90304.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200149-13568.gif)
已知椭圆C的中心在原点、焦点在
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200138-30832.gif)
(Ⅰ)求椭圆C的标准方程;
(Ⅱ)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200138-92805.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200139-99114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200139-69809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200138-92805.gif)
如图,在直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200120-10873.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200121-57068.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200121-38973.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200121-91146.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200121-88172.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200122-52304.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200122-19978.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200122-19978.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200122-38220.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200121-57068.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200122-91633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200123-44283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200123-20062.gif)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200121-57068.gif)
(2)设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200121-57068.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200123-99350.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200123-64903.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200124-35332.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200124-10602.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200124-35332.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200123-64903.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200121-57068.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200124-46693.jpg)
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