题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165626-17126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165626-81844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165626-21854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165627-29385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165627-74788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165627-99415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165627-42223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165628-62367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165628-11225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165628-28669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165628-44690.png)
(1) 求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165628-11225.png)
(2) 是否存在过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-10018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-42607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165628-11225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-66934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-92042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-42607.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-99225.png)
又原点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165627-74788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165627-99415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165627-42223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165630-40566.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165630-43282.png)
故椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165630-25571.png)
(2)显然当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-42607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165628-62367.png)
故可设存在满足条件的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-42607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165630-24290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165628-11225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165631-86800.png)
因为直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-42607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165628-11225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-66934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-66934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165631-51917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165631-92794.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165631-33471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165631-44155.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165632-76733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165632-85314.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165632-16788.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165632-12761.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-66934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165633-58377.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165633-68044.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165633-19888.png)
所以存在满足条件的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165629-42607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165633-40222.png)
解析
核心考点
试题【已知椭圆的右焦点为且,设短轴的一个端点为,原点到直线的距离为,过原点和轴不重合的直线与椭圆相交于两点,且.(1) 求椭圆的方程;(2) 是否存在过点的直线与椭圆】;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/20191023/20191023165623-49114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165613-49827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165613-83221.png)
A.1 | B.2 | C.3 | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165608-95350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165608-42650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165608-15889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165608-61806.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165608-42650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165608-61806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165609-11904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165609-57759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165609-12443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165600-20157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165600-71580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165600-27825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165600-74215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165600-38840.png)
(Ⅰ)求椭圆C的离心率
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165600-22028.png)
(Ⅱ)若已知点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165600-62499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165600-46408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165601-98452.png)
求椭圆C的方程。
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165551-97045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165551-54490.png)
A.锐角三角形 | B.直角三角形 | C.钝有三角形 | D.随m、n变化而变化 |
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