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
名校
解题方法
3 . 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
4 . 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
5 . 如图,水平面上摆放了两个棱长为
的正四面体
和
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/517b51b4-6e4f-48fb-8018-bf1ed33ee98c.png?resizew=242)
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6d7e887348f80fda1e157e0222573d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a009fe059af6b399cb5c49839a0511.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/517b51b4-6e4f-48fb-8018-bf1ed33ee98c.png?resizew=242)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb780dea4bb7d09bf3cb08b7258ebbb1.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c506e1806d697fff2602f72db1ccd7.png)
您最近一年使用:0次
2023-01-10更新
|
206次组卷
|
3卷引用:山西省运城市2022-2023学年高三上学期期末调研测试数学试题
名校
6 . 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
解题方法
7 . 已知抛物线
的焦点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/9c3a29c6-c76c-45ba-b61c-be95080b7958.png?resizew=167)
(1)如图所示,线段
为过点
且与
轴垂直的弦,动点
在线段
上,过点
且斜率为1的直线
与抛物线交于
两点,请问
是否为定值,若是,求出该定值;若不是,说明理由;
(2)过焦点
作直线
与
交于
两点,分别过
作抛物线
的切线,已知两切线交于点
,求证:直线
、
、
的斜率成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/9c3a29c6-c76c-45ba-b61c-be95080b7958.png?resizew=167)
(1)如图所示,线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8141a4a565a9b1e56bf710b84476a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6e75677951ef1388f76aee5a779149.png)
(2)过焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95add8635f609e7fdc0a423842f7d037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95add8635f609e7fdc0a423842f7d037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1ab8833d1823f3dc027a39bdb58e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1a6ce0b35896c8a1c687a4376e71f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75af77f184b8d76a881874298852081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ad3d1bc78e0ea7a5518f38c0cf5b30.png)
您最近一年使用:0次
2023-01-10更新
|
1212次组卷
|
4卷引用:山西省运城市2022-2023学年高三上学期期末调研测试数学试题
山西省运城市2022-2023学年高三上学期期末调研测试数学试题山西省吕梁市2023届高三上学期期末数学试题(已下线)专题3 解答题题型(已下线)安徽省江南十校2022届高三下学期3月一模理科数学试题变式题16-20
名校
解题方法
8 . 如图,正方形
和矩形
所在的平面互相垂直,
,
,
是线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/10abf3ff-e569-4b11-8802-8bdf95b1896b.png?resizew=196)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求平面
与平面
夹角的余弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cee0f36dc452e58086832c0152b641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/10abf3ff-e569-4b11-8802-8bdf95b1896b.png?resizew=196)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
您最近一年使用:0次
2022-01-22更新
|
401次组卷
|
2卷引用:山西省运城市康杰中学2021-2022学年高二上学期期末数学试题
名校
9 . 如图,四棱柱
中,平面
平面
,底面
为菱形,
与
交于点O,
.
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992613741322240/2995556340269056/STEM/33c76a39-6559-4d7d-9792-b19f7a924fa9.png?resizew=276)
(1)求证:
平面
;
(2)线段
上是否存在点F,使得
与平面
所成角的正弦值是
?若存在,求出
;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ba5715a95b8de18c637c12c3d30d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f435b981d18b1ba02cb78ff404496c29.png)
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992613741322240/2995556340269056/STEM/33c76a39-6559-4d7d-9792-b19f7a924fa9.png?resizew=276)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ad2917b716db41c03e670f77d411d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239198e40085b7dcffbe747c9c265a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a3fd10496f99992b2b6de9f4f6e34ed.png)
您最近一年使用:0次
2022-06-06更新
|
761次组卷
|
8卷引用:山西省运城市2022-2023学年高二上学期期末数学试题
解题方法
10 . 已知
为坐标原点,抛物线C:
的焦点为F,P为抛物线C上一点,PF与y轴垂直,Q为y轴上一点,且
,若
.
(1)求
;
(2)设点
,过点
作两条不同的直线分别交抛物线C于A,B两点和D,E两点,且满足
,求证
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad780ce9bac48bc3027bc343e7dc8556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693d0d0814e022413c3018f0ee25d4a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e584f799ea554fc5533925ead4672501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5421aa8aa91be1ed4d3ea9e3635f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b82e181268050d93d192e3dc086c26.png)
您最近一年使用:0次