解题方法
1 . 已知椭圆
的左、右焦点分别为
,设点
,在
中,
.
(1)求椭圆C的方程;
(2)设P,Q为C上异于点A的两动点,记直线AP,AQ的斜率分别为
,若
,求证:直线PQ过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e756feec2851b90497421790a7206e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfdab8b0494d22a788fd0a34258abd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fedcf44928a090ad5553edf8a0fd7c.png)
(1)求椭圆C的方程;
(2)设P,Q为C上异于点A的两动点,记直线AP,AQ的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe91cc3bfc93ef1cc3369fa6756bbd4d.png)
您最近一年使用:0次
2 . 如图,在三棱柱
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/c7e4b942-6b27-4786-a3aa-48b116e85f84.png?resizew=157)
(1)求证:
平面
;
(2)若
,直线AB与平面
所成的角为
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4759c765972e2e039b295a0d0d4fc840.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/c7e4b942-6b27-4786-a3aa-48b116e85f84.png?resizew=157)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900e00a3609e6043af1034761d4d65f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ab602944bedd4fe63d0575178dfdb8.png)
您最近一年使用:0次
3 . 已知椭圆
的离心率为
,直线
过E的上顶点和右焦点,直线
过E的右顶点,
,
与
之间的距离为
.
(1)求椭圆E的标准方程.
(2)已知过原点的直线与椭圆E交于A,B两点,点C是E上异于A,B的点,且
,试问在x轴上是否存在点M,使得点M到直线AC的距离为定值?若存在,求出定值与点M的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1095c036b49c3327baaa2c3c7f746134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95c6372ea779d23524d4b2173dc5aa3.png)
(1)求椭圆E的标准方程.
(2)已知过原点的直线与椭圆E交于A,B两点,点C是E上异于A,B的点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4540450e06cdcb8e4405c2c154853f8.png)
您最近一年使用:0次
2024-01-22更新
|
736次组卷
|
5卷引用:山西运城盐湖区第五高级中学2024届高三上学期期末数学试题
名校
解题方法
4 . 如图,直三棱柱
中,
为等腰直角三角形,
,E,F分别是棱
上的点,平面
平面
,M是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/130f51e7-22c1-4148-886e-06e411f590ef.png?resizew=136)
(1)证明:
平面
;
(2)若
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d89ba4036a5d18ec4abed44d7fd8e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e86e3991200297ad172455e5ea93f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/130f51e7-22c1-4148-886e-06e411f590ef.png?resizew=136)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0684e0b09b04661c602437982c0397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d557872d3299577be8c5872ba1ae5b59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2023-12-20更新
|
643次组卷
|
4卷引用:山西运城盐湖区第五高级中学2024届高三上学期期末数学试题
5 . 如图,在圆柱体
中,
,
,劣弧
的长为
,AB为圆O的直径.
(1)在弧
上是否存在点C(C,
在平面
同侧),使
,若存在,确定其位置,若不存在,说明理由;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e90a7898ed4e02bcdec4457b6d4ff5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/5/17e89554-8bd0-4d15-95fa-a71350a8d9a1.png?resizew=167)
(1)在弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d39a49fa46a594b3634381b17323c8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7768503b1ad4775258b2f1a71c413086.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b18e27dd9296b846151a4eab1972a.png)
您最近一年使用:0次
2023-09-04更新
|
226次组卷
|
2卷引用:山西省运城市2024届高三上学期期末调研测试数学试题
解题方法
6 . 已知椭圆
的焦距为
,左、右顶点分别为
,上顶点为B,且
.
(1)求椭圆C的方程;
(2)若过
且斜率为k的直线l与椭圆C在第一象限相交于点Q,与直线
相交于点P,与y轴相交于点M,且
.求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1735708848cfde06947647a29687a76.png)
(1)求椭圆C的方程;
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f69a7effc74ab83bd02bb4c2d9e9716.png)
您最近一年使用:0次
2023-04-23更新
|
306次组卷
|
3卷引用:山西省运城市2024届高三上学期期末调研测试数学试题
7 . 已知抛物线
,其上一点
到焦点
的距离为
.
(1)求
的标准方程;
(2)若直线
与抛物线
交于
、
两点,且以
为直径的圆与
轴相切,求该圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5975ba4e093e3eed64434596d945d4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738053bd0217fad1657515ea93464471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54623bccef254857ad663fe6d18f320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2023-02-16更新
|
186次组卷
|
2卷引用:山西省运城市2022-2023学年高二上学期期末数学试题
8 . 已知椭圆
的左右焦点分别为
,椭圆C经过点
,且直线
,与圆
相切.
(1)求椭圆C的方程;
(2)直线
与椭圆C交于P,Q两点,点M在x轴上,且满足
,求点M横坐标的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
(1)求椭圆C的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53cd24fdb222c2e68c05c21600383df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db64a7467f0abcfe06cc9b279a5be7c.png)
您最近一年使用:0次
2023-02-03更新
|
283次组卷
|
3卷引用:山西省运城市稷山县稷王中学等3校2023届高三上学期期末数学试题
9 . 如图,在三棱锥
中,平面
平面
,
,O为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/05da39df-3d0f-4c21-a917-59db0fd72ca1.png?resizew=187)
(1)证明:
;
(2)若
是边长为1的等边三角形,点E在棱
上,
,且二面角
的大小为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/05da39df-3d0f-4c21-a917-59db0fd72ca1.png?resizew=187)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bb2d945b7908ebac080e6595d4895f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d76c5ac5c9f0a2ec064487c02c476e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324d453870b345da0c41977290192f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
您最近一年使用:0次
2023-02-03更新
|
350次组卷
|
2卷引用:山西省运城市稷山县稷王中学等3校2023届高三上学期期末数学试题
名校
10 . 如图,在圆柱
中,CE是圆柱的一条母线,ABCD是圆O的内接四边形,AB是圆O的直径,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/21/cbe55526-e380-44f7-a94c-04db8e6d2f05.png?resizew=137)
(1)若
,求证:
平面CEO;
(2)若
,求直线BE与平面ADE所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3402ea855e2ae2dcd98f607bef4fdd6c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/21/cbe55526-e380-44f7-a94c-04db8e6d2f05.png?resizew=137)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5edfe97aeab0cf16b40fa9d2e15f9e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba7be04bdcbb90d6b49ce9e14cda9bb.png)
您最近一年使用:0次