真题
1 . 如图,四棱锥
中,底面是以
为中心的菱形,
底面
,
,
为
上一点,且
.
(1)求
的长;
(2)求二面角
的正弦值.
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571784957353984/1571784963276800/STEM/c2f70fe100034862ad6a8d5165d3db75.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571784957353984/1571784963276800/STEM/9874f5fd78824379bc461e831765222c.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571784957353984/1571784963276800/STEM/666341487fc24fe894dd5693b5423d70.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571784957353984/1571784963276800/STEM/c285cf021e4146ea9257c0acf215d626.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571784957353984/1571784963276800/STEM/5e24b055d96e44bfb1379179ae66437d.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571784957353984/1571784963276800/STEM/e8e14784d9d94c5298c601d73e447b85.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571784957353984/1571784963276800/STEM/a83d9b34c6924cca9a9813d7d0411cf1.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571784957353984/1571784963276800/STEM/0b2dbced52bc4937b20069a722f436af.png)
(1)求
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571784957353984/1571784963276800/STEM/542f6e6aab214cde92cb47df27649862.png)
(2)求二面角
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571784957353984/1571784963276800/STEM/e480f142b1dd41fd9ababe1b594f8627.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/c5a93352-2096-4256-abb2-0c6023565c6a.png?resizew=218)
您最近一年使用:0次
真题
2 . 如图,椭圆的中心为原点0,离心率e=
,一条准线的方程是x=2![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759047401472/1571759053062144/STEM/b7e1a454e09749c2b542b6ce659ee2a9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/891933f5-6152-43cb-a3a7-ac70f2ed9f10.png?resizew=196)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)设动点P满足:
=
+2
,其中M、N是椭圆上的点,直线OM与ON的斜率之积为﹣
,
问:是否存在定点F,使得|PF|与点P到直线l:x=2
的距离之比为定值;若存在,求F的坐标,若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759047401472/1571759053062144/STEM/26f6cbbe162947659993fc8b1df609f8.png)
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759047401472/1571759053062144/STEM/b7e1a454e09749c2b542b6ce659ee2a9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/891933f5-6152-43cb-a3a7-ac70f2ed9f10.png?resizew=196)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)设动点P满足:
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759047401472/1571759053062144/STEM/9f528361df2b402a993b0993844cf190.png)
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759047401472/1571759053062144/STEM/37c8afbf569d4533ba61b129f7204f7e.png)
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759047401472/1571759053062144/STEM/fc26f668442a446cb0e41884bf54ff71.png)
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759047401472/1571759053062144/STEM/82308a340ff84905ae54c9663a9fd30d.png)
问:是否存在定点F,使得|PF|与点P到直线l:x=2
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759047401472/1571759053062144/STEM/dec6899f04f84117b29f8f2f069d1a09.png)
您最近一年使用:0次
真题
3 . 已知以原点
为中心的双曲线的一条准线方程为
,离心率
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/94f45164-6bd4-478d-a16c-ce1716afecab.png?resizew=143)
(Ⅰ)求该双曲线的方程;
(Ⅱ)如图,点
的坐标为
,
是圆
上的点,点
在双曲线右支上,求
的最小值,并求此时
点的坐标
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569629514579968/1569629643350016/STEM/5c0e6a2812344e06bea44428748e480d.png)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569629514579968/1569629643350016/STEM/303e5fade29a4ccf8bc2ae965d8fffc6.png)
![](https://img.xkw.com/dksih/QBM/2010/3/9/1569629514579968/1569629643350016/STEM/d25a6aa53d4d42d99384f72f030b1de2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/94f45164-6bd4-478d-a16c-ce1716afecab.png?resizew=143)
(Ⅰ)求该双曲线的方程;
(Ⅱ)如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b759a68434e8af4db741b9c939e423f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742b4467ef84c43e2d119a8573d5f0b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b17e28ce88e9a94b0584fed68b4adf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2016-11-30更新
|
2156次组卷
|
4卷引用:2009年普通高等学校招生全国统一考试文科数学(重庆卷)
2009年普通高等学校招生全国统一考试文科数学(重庆卷)(已下线)2.3.2+双曲线的简单几何性质(2)(重点练)-2020-2021学年高二数学(理)十分钟同步课堂专练(人教A版选修2-1)(已下线)2.2.2+双曲线的简单几何性质(2)(重点练)-2020-2021学年高二数学(文)十分钟同步课堂专练(人教A版选修1-1)(已下线)3.2.2 双曲线的简单几何性质(2)(重点练)-2020-2021学年高二数学十分钟同步课堂专练(人教A版选择性必修第一册)
真题
4 . 已知以原点
为中心的椭圆的一条准线方程为
,离心率
,
是椭圆上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/7435deca-b79b-4274-aa97-e273b49b8e56.png?resizew=176)
(Ⅰ)若
的坐标分别是
,求
的最大值;
(Ⅱ)如图,点
的坐标为
,
是圆
上的点,
是点
在
轴上的射影,点
满足条件:
,
,求线段
的中点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9e2f49f199375491aaf131d2df5a5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/7435deca-b79b-4274-aa97-e273b49b8e56.png?resizew=176)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76c5a0c8dff254d560ab24e51e0b136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165e9df534b004490018dbaf4240d223.png)
(Ⅱ)如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e754460fcfbe39b6f09eb5e27c189664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb51bc1539d761ca19661ae5c015edaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
真题
5 . 如图,M(-2,0)和N(2,0)是平面上的两点,动点P满足: ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df52aad5508a305ac9bf1e7960b547b7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/1b718465-bc57-41e0-95f4-47110a05b4d1.png?resizew=198)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df52aad5508a305ac9bf1e7960b547b7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/1b718465-bc57-41e0-95f4-47110a05b4d1.png?resizew=198)
(Ⅰ)求点P的轨迹方程;
(Ⅱ)设d为点P到直线l: 的距离,若
,求
的值.
您最近一年使用:0次
2016-11-30更新
|
1415次组卷
|
2卷引用:2008年普通高等学校招生全国统一考试文科数学(重庆卷)