解题方法
1 . 在如图所示的几何体中,四边形
是边长为2的正方形,四边形
是梯形,
平面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/95f71800-0f86-4350-8049-55140a02a7c5.png?resizew=152)
(1)求证:平面
平面
;
(2)求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7bce6eba5d07a34f24c5370c580ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd3bab1f8326d07ec9c6503cd948b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9420912b53d9f512b396870881c53db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/95f71800-0f86-4350-8049-55140a02a7c5.png?resizew=152)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c606f78391198b6648ba0b92b60f8cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1956db288a5a3b8c97d2539e9e5e4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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解题方法
2 . 如图,在直三棱柱
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/f382c9d0-f7a8-4a45-92f8-25e38f1445d0.png?resizew=172)
(1)若
,求直线
与直线
所成角的余弦值;
(2)若
为线段
上一点,且
,当
时,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ec1f257f2d002548da1c3287d0dc75.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/f382c9d0-f7a8-4a45-92f8-25e38f1445d0.png?resizew=172)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b6bd6c0803ddf8240e67d22a07a7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84a436704964dc76f16c2c23665ab3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
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解题方法
3 . 已知抛物线C:
的焦点到准线的距离为2,圆M与y轴相切,且圆心M与抛物线C的焦点重合.
(1)求抛物线C和圆M的方程;
(2)设
为圆M外一点,过点P作圆M的两条切线,分别交抛物线C于两个不同的点
,
和点
,
,且
.证明:点P在一条定曲线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
(1)求抛物线C和圆M的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6502f80a31bfffe5dfdb2f6ffe5ef2c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d14d14310aaf4630c169e8d7b2a9cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34494f6910d4e081d89d1136c8cdff4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f0f4943e96860f1043fbdd9588531b.png)
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4 . 已知椭圆E:
过点
,且左,右焦点分别为
,
,直线y=kx与椭圆交于A,B两点.
(1)求椭圆E的方程;
(2)若椭圆上一动点
,使得
,求点P的横坐标x的取值范围.
(3)设
为椭圆上一点,且直线NA的斜率
,试求直线NB的斜率
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13683e2ecf2164a0adbfdb9923d210a3.png)
(1)求椭圆E的方程;
(2)若椭圆上一动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30048d0783f2ad1d15c0fec010afdfea.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffbca194ac467f226654cbd444a1813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de39032596310def1b2dadb9a917dc3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
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2023-07-03更新
|
324次组卷
|
3卷引用:黑龙江省饶河县高级中学2022-2023学年高二下学期期末考试数学试题
5 . 如图,椭圆
和圆
,已知圆
将椭圆
的长轴三等分,椭圆
右焦点到右顶点的距离为
,椭圆
的下顶点为E,过坐标原点O且与坐标轴不重合的任意直线l与圆
相交于点A,B.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/42d9488b-c6e8-4aa9-ab78-02cefeb5311f.png?resizew=258)
(1)求椭圆
的方程;
(2)若直线
分别与椭圆
相交于另一个交点为点P,M.求证:直线
经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630cb5e3f23369a875a2b76a5501ea36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1b1ce092493086f74481b7d6dd9434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/42d9488b-c6e8-4aa9-ab78-02cefeb5311f.png?resizew=258)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57445efa8ad1501d049e551f34a158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
您最近一年使用:0次
2023-02-03更新
|
1098次组卷
|
4卷引用:黑龙江省佳木斯市第一中学2022-2023学年高二上学期期末数学试题
名校
解题方法
6 . 如图,在正方体
中,E是棱
上的点(点E与点C,
不重合).
(1)在图中作出平面
与平面ABCD的交线,并说明理由;
(2)若正方体的棱长为1,平面
与平面ABCD所成锐二面角的余弦值为
,求线段CE的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/28/44e1db2d-3cdb-4d89-8b8d-4c6809dd2361.png?resizew=153)
(1)在图中作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
(2)若正方体的棱长为1,平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9662368fd788afb77b79035cdd268b.png)
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2023-06-24更新
|
584次组卷
|
4卷引用:黑龙江省大庆市萨尔图区第二十三中学2022-2023学年高二下学期期末数学试题
黑龙江省大庆市萨尔图区第二十三中学2022-2023学年高二下学期期末数学试题江西省上饶市广丰区私立康桥中学2023-2024学年高二上学期期末模拟数学试题贵州省安顺市2022届高三第一次教学质量监测统一考试数学(理)试题(已下线)1.4.2 用空间向量研究距离、夹角问题(AB分层训练)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)
名校
7 . 如图,四棱锥
中,
平面
、底面
为菱形,E为PD的中点.
![](https://img.xkw.com/dksih/QBM/2023/1/19/3156092819922944/3158518859284480/STEM/17321696cd5d446abc29fd816c451ec0.png?resizew=167)
(1)证明:
平面
;
(2)设
,
,菱形ABCD的面积为
,求平面AED与平面AEC夹角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2023/1/19/3156092819922944/3158518859284480/STEM/17321696cd5d446abc29fd816c451ec0.png?resizew=167)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5748c32be75256e6c83b7832ff7264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
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8 . 如图,在四棱锥
中,底面ABCD为正方形,
,平面
平面
,N是CD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/24/9988b1dd-fff3-4a53-aeed-97cf11902b61.png?resizew=160)
(1)若点M为线段PD上一点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
平面AMN,求
的值;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fcc62f1c0536d8f82409e8c8df7beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/24/9988b1dd-fff3-4a53-aeed-97cf11902b61.png?resizew=160)
(1)若点M为线段PD上一点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced22fbe85d4a749c7b0b6bbae3ea3e7.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a4bddf1ea3c5d37f2233a4821909e9.png)
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解题方法
9 . 已知椭圆
的左、右焦点分别为
、
,点P在椭圆E上,
,且
.
(1)求椭圆的标准方程;
(2)直线
与椭圆E相交于A,B两点,与圆
相交于C,D两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dfb22c6f1c155747100e7536cd1abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29aa3bd463abf39a3f63e077abcc28.png)
(1)求椭圆的标准方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee478c8ced07e292d1fadc39f2fec39b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf6f64871b0148d887f64ee456f826d.png)
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10 . 已知A,B分别为双曲线
的左、右顶点,M为双曲线E上异于A、B的任意一点,直线MA、MB斜率乘积为
,焦距为
.
(1)求双曲线E的方程;
(2)P为直线
上的动点,若直线PA与E的另一交点为C,直线PB与E的另一交点为D.证明:直线CD过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabd197d769d62408b492ab538eedd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbff61fe9d4e93d7cc338489d1c99c40.png)
(1)求双曲线E的方程;
(2)P为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
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