题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045042-23908.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045042-89896.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045042-89896.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045042-13604.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045042-35433.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045042-40557.gif)
(I)证明
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045043-71035.gif)
(II)若动点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045043-92950.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045043-26315.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045043-57595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045043-92950.gif)
答案
(1)略
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-13967.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-17341.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-45306.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-37184.gif)
(I)当
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-44890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045045-40718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045042-13604.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045045-73687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045045-77344.gif)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045045-79463.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-44890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045045-40718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-44890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045045-96470.gif)
代入
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045042-23908.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045046-33437.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045046-69117.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045046-81650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045046-87410.gif)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045047-56993.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045047-66390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045047-60700.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045047-74850.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045047-38304.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045048-43757.gif)
(II)解法一:设
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045048-56841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045048-67047.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045048-57666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045049-46738.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045049-70652.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045043-26315.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045049-83099.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045049-77295.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-44890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045049-41687.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-44890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045045-40718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045050-76050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045050-93610.gif)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045042-13604.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045050-89282.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045050-80017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045051-10952.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045051-34588.gif)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045050-93610.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-13967.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-44890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045045-40718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045051-17202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045051-45842.gif)
所以点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045043-92950.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-13967.gif)
解法二:同解法一得
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045049-77295.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-44890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045045-40718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045046-81650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045051-65307.gif)
由①、②、③得
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045052-80890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045052-23186.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045052-44771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045052-77361.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045053-46623.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045053-13889.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-13967.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045053-59011.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045043-92950.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045053-34034.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-44890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045045-40718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045051-17202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045051-45842.gif)
故点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045043-92950.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045044-13967.gif)
核心考点
试题【(文科)已知双曲线的右焦点为,过点的动直线与双曲线相交于两点,点的坐标是.(I)证明为常数;(II)若动点满足(其中为坐标原点),求点的轨迹方程.】;主要考察你对双曲线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/20191024/20191024045030-16480.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045030-49554.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045030-70393.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045030-28528.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045030-56684.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045030-28528.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045031-65155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045031-71348.gif)
(1)求双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045030-28528.gif)
(2)无论直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045030-56684.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045031-65155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045030-28528.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045031-34826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045031-69947.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045031-34826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045025-28266.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045025-81109.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045026-53208.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045026-31105.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045026-51327.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045026-68187.gif)
A.2或6 | B.6 | C.2 | D.7 |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045017-47861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045017-36450.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045017-43270.gif)
一点,若
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045018-32084.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045018-67590.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045013-75980.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045013-70398.gif)
(Ⅰ)求证:点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045013-70398.gif)
(Ⅱ)设点A的坐标为(3,0),求
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045013-30869.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045010-62411.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045010-32234.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045010-13905.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024045011-69142.gif)
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