名校
1 . 如图,在四棱锥
中,平面
平面PAD,
,
,
,
,
,E是PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/75999df6-7b26-4bc9-b456-9eece69fa814.png?resizew=168)
(1)求证:
;
(2)若点M在线段PC上,异面直线BM和CE所成角的余弦值为
,求面MAB与面PCD夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7ae4091a3a2767fde8e9f5a604c1a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646d135e77c1ea69390d9e937f88b85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/75999df6-7b26-4bc9-b456-9eece69fa814.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/371853a703a8dafa6f8e942f46cb8706.png)
(2)若点M在线段PC上,异面直线BM和CE所成角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
您最近一年使用:0次
2022-12-27更新
|
2197次组卷
|
7卷引用:山东省莱西市第一中学2022-2023学年高二学业水平检测(二) 数学试题
2 . 已知抛物线
的焦点为F,过点F的直线l交抛物线C于M,N两点,交y轴于P点,点N位于点M和点P之间.
(1)若
,求直线l的斜率;
(2)若
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece74a1c672383a4d03363f376d060f8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0b05f17a40e21dfc915a7e9debfa61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
3 . 已知椭圆
的中心在坐标原点
,焦点在
轴上,左、右焦点分别为
、
,离心率
,短轴长为2,.
(1)求椭圆
的标准方程;
(2)设过
且斜率不为零的直线
与椭圆
交于
、
两点,过
作直线
的垂线,垂足为
,证明:直线
恒过一定点,并求出该定点的坐标;
(3)过点
作另一直线
,与椭圆分别交于
、
两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/b9ea9f5967c96e60f03f332fd792cd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9d2abf13c2842f58654abf73c6b4ee.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e1ba8ef888dfe9a639dddd38d6d603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ae93479f71c86ffa37131326cfd993.png)
您最近一年使用:0次
2021-12-10更新
|
1117次组卷
|
3卷引用:2021年黑龙江省哈尔滨市第三中学校高二上学期期中数学试题
2021年黑龙江省哈尔滨市第三中学校高二上学期期中数学试题江西省赣州市赣县第三中学2021-2022学年高二12月月考数学(理)试题(已下线)易错点12 圆锥曲线-备战2022年高考数学考试易错题(新高考专用)
名校
4 . 如图,已知直线
与抛物线
相交于
两点,
为坐标原点,直线
与
轴相交于点
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/6a7bd406-cac7-4ad3-b182-be6aac0a5ffa.png?resizew=187)
(1)求证:
;
(2)求点
的横坐标;
(3)过
点分别作抛物线的切线,两条切线交于点
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1615e8b8f85e033b3b19ed444a5177a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d681a7a9830fe11598654e141aa28e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/6a7bd406-cac7-4ad3-b182-be6aac0a5ffa.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44cd27618651d7c3b2655d76d1273ea.png)
您最近一年使用:0次
2020-03-13更新
|
359次组卷
|
2卷引用:2019届黑龙江省学业水平考试数学(理科)试卷
2020高三·江苏·专题练习
5 . 已知椭圆E:
+
=1(a>b>0)的离心率为
,焦点到相应准线的距离为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/391632be-5af3-4ef3-a312-e146bb15b6b8.png?resizew=186)
(1) 求椭圆E的标准方程;
(2) 已知P(t,0)为椭圆E外一动点,过点P分别作直线l1和l2,直线l1和l2分别交椭圆E于点A,B和点C,D,且l1和l2的斜率分别为定值k1和k2,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7355be4fcbc3130a5951364a3be76d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5268413295580cfda0755ab458b36b64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/391632be-5af3-4ef3-a312-e146bb15b6b8.png?resizew=186)
(1) 求椭圆E的标准方程;
(2) 已知P(t,0)为椭圆E外一动点,过点P分别作直线l1和l2,直线l1和l2分别交椭圆E于点A,B和点C,D,且l1和l2的斜率分别为定值k1和k2,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2efd9f1d286d417d5596e4fa2b52a4.png)
您最近一年使用:0次
12-13高二上·福建泉州·期末
名校
6 . 已知,椭圆
过点
,两个焦点为
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)
是椭圆
上的两个动点,如果直线
的斜率与
的斜率互为相反数,证明直线
的斜率为定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e90064d012356de1877aa697cd6d6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6917df35ab960d5958af89095219434.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
2016-12-03更新
|
3300次组卷
|
18卷引用:2011-2012学年福建省南安市侨光中学高二上学期期末文科数学试卷
(已下线)2011-2012学年福建省南安市侨光中学高二上学期期末文科数学试卷(已下线)2011-2012学年广东省深圳高级中学高二上学期期末考试文科数学试卷(已下线)2012-2013学年安徽省马鞍山市第二中学高二下学期期中考试文科数学试卷(已下线)2012-2013学年安徽省涡阳四中高二下第三次(期末)质检文科数学卷(已下线)2013-2014学年广东省执信中学高二下学期期中文科数学试卷2015-2016学年山西省运城市高二上学期期末理科数学试卷【全国百强校】山东省泰安第一中学2019届高三12月学情诊断数学(文)试题广东省汕头市2018-2019学年高二下学期期中数学(理)试题浙江省金华市曙光学校2019-2020学年高三下学期返校测试数学试题(已下线)秒杀题型11 圆锥曲线中的定值与定点-2020年高考数学试题调研之秒杀圆锥曲线压轴题山东省淄博市淄川中学2018-2019学年高二6月月考数学试题(已下线)专题3-5 圆锥曲线定值问题江西省丰城中学2022-2023学年下学期高二入学考试数学试题(已下线)第五篇 向量与几何 专题6 调和线束 微点1 调和线束(一)(已下线)第五篇 向量与几何 专题10 圆锥曲线中的四点共圆问题 微点2 圆锥曲线中的四点共圆问题(二)北京市丰台区第二中学2024届高三上学期开学考数学试题2023年山西省运城市景胜中学业水平考试数学试题专题08B圆的方程与圆锥曲线