1 . 已知动圆E经过定点D(1,0),且与直线x=-1相切,设动圆圆心E的轨迹为曲线C.
(1)求曲线C的方程;
(2)设过点P(1,2)的直线l1,l2分别与曲线C交于A,B两点,直线l1,l2的斜率存在,且倾斜角互补,证明:直线AB的斜率为定值.
(1)求曲线C的方程;
(2)设过点P(1,2)的直线l1,l2分别与曲线C交于A,B两点,直线l1,l2的斜率存在,且倾斜角互补,证明:直线AB的斜率为定值.
您最近一年使用:0次
2020-12-07更新
|
1088次组卷
|
11卷引用:新疆部分地区2024届高三高考素养调研第二次模拟考试数学试题
(已下线)新疆部分地区2024届高三高考素养调研第二次模拟考试数学试题【全国省级联考】黑龙江省2018届高三仿真模拟(四)数学(理科)试题【全国省级联考】黑龙江省2018年普通高等学校招生全国统一考试仿真模拟(四)数学(文科)试卷安徽省阜阳市颍州区第三中学2019-2020学年高二上学期期末数学(文)试题(已下线)专题9.9 圆锥曲线的综合问题(精练)-2021年高考数学(理)一轮复习讲练测(已下线)【新教材精创】3.3.2+抛物线的简单几何性质(2)+导学案-人教A版高中数学选择性必修第一册(已下线)第九单元 解析几何(B卷 滚动提升检测)-2021年高考数学(理)一轮复习单元滚动双测卷(已下线)第九课时 课后 3.3.2 第2课时 抛物线的方程及性质的应用沪教版(2020) 选修第一册 精准辅导 第2章 2.4(2) 抛物线的性质云南省大理市大理州实验中学2021-2022学年高二下学期见面考试数学试题广东省茂名市高州中学2023-2024学年高二下学期3月滚动测试数学试题
解题方法
2 . 如图所示,四棱柱
的侧棱与底面垂直,底面
是菱形,四棱锥
的顶点
在平面
上的投影恰为四边形
对角线的交点
,四棱锥
和四棱柱
的高相等.
![](https://img.xkw.com/dksih/QBM/2020/7/30/2516895519547392/2517208957730816/STEM/a4be1ec7662c4b08941b126c4548be9b.png?resizew=182)
(1)证明:
平面
;
(2)若
,
,求平面
与平面
所成的二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/2020/7/30/2516895519547392/2517208957730816/STEM/a4be1ec7662c4b08941b126c4548be9b.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fc25927a6862b6643bcfebefc44873.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb8fb552b9e21dbaba74d11aa747790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4afa61e0bcb124aec52ad0cc84fd94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3da630440d6d416f19ee22c8431c882.png)
您最近一年使用:0次
2020-07-30更新
|
340次组卷
|
3卷引用:新疆乌鲁木齐市2024届高三高考模拟测试数学试题
解题方法
3 . 如图,在四棱锥
中,四边形
为梯形,且AB
DC,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/29/4e9f54d7-9df7-4c57-b74a-04b4a8aad691.png?resizew=209)
(Ⅰ)证明:平面
平面
;
(Ⅱ)若
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/29/4e9f54d7-9df7-4c57-b74a-04b4a8aad691.png?resizew=209)
(Ⅰ)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ad6a0124359e8b9f7649cf0bff51ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f04579e4c69a5b6b895e0c44a94532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83c3f76bc7569c3c088da98bb3b2c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
您最近一年使用:0次
2020-05-09更新
|
280次组卷
|
2卷引用:2020届新疆高三第一次模拟测试(问卷)数学(理科)试题
名校
4 . 如图,在三棱柱
中,
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/1086a6ac-8473-4a59-a0a7-82ab95af2f97.png?resizew=164)
(1)证明:
平面ABC.
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fd676c41d2d644928f014b0fea4689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518a322494bd7624e6eed7fe290a2f9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/1086a6ac-8473-4a59-a0a7-82ab95af2f97.png?resizew=164)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89195bacd53d43195e70c12b5cfa041.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a824c242050a27d9da3bb3276ea99170.png)
您最近一年使用:0次
2020-07-11更新
|
430次组卷
|
4卷引用:新疆昌吉州2022届高三第二次诊断性测试数学(理)试题
5 . 如图,在三棱锥P-ABC中,
,
,
平面PAB,D,E分别是AC,BC上的点,且
平面PAB.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/1995a7a2-5ec0-44a1-b8e0-7d86cdec1c9d.png?resizew=242)
(1)求证
平面PDE;
(2)若D为线段AC中点,求直线PC与平面PDE所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23848b4957209461233d35671773e89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/1995a7a2-5ec0-44a1-b8e0-7d86cdec1c9d.png?resizew=242)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
(2)若D为线段AC中点,求直线PC与平面PDE所成角的正弦值.
您最近一年使用:0次
6 . 如图,将等腰直角三角形
沿斜边上的高
翻折,使二面角
的大小为
,翻折后
的中点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/eecfe303-57bb-4202-aff7-0836bd195b57.png?resizew=285)
(Ⅰ)证明
平面
;
(Ⅱ)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29cc627d76412c236aac6b29fa0fdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/eecfe303-57bb-4202-aff7-0836bd195b57.png?resizew=285)
(Ⅰ)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c079889aea502b5783046f78728eb1.png)
您最近一年使用:0次
2020-06-20更新
|
411次组卷
|
2卷引用:新疆乌鲁木齐地区2020届高三年级第三次质量监测理科数学试题
7 . 如图,在四棱锥
中,底面
是正方形,
平面
,且
,点
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/725cef74-5146-4fd0-9650-eba152709436.png?resizew=163)
(1)求证:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/c3b10835116b9b777a666b438c907b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/725cef74-5146-4fd0-9650-eba152709436.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5102c216393e133fa25dba98cd78535.png)
您最近一年使用:0次
2019-11-21更新
|
1030次组卷
|
7卷引用:新疆维吾尔自治区乌鲁木齐市第一中学2023届高三第三次诊断性测试数学(理)试题
8 . 如图,在四棱锥
中,
平面
,
是正方形,
是
中点,点
在
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/5632ee9f-5143-492f-ba63-10f0f736f2ca.png?resizew=198)
(1)证明
平面
;
(2)若
,求平面
与平面
所成二面角的正弦值.
![](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://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4f947e0f238c37854afa0bf6b93a8d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/5632ee9f-5143-492f-ba63-10f0f736f2ca.png?resizew=198)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b37cff3ef72ff9386cebea4f2792bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
您最近一年使用:0次
2020-03-20更新
|
301次组卷
|
2卷引用:2020届新疆乌鲁木齐地区高三年级第一次质量监测理科数学试题
9 . 如图1,在梯形ABCD中,
,
,
,过A,B分别作CD的垂线,垂足分别为E,F,已知
,
,将梯形ABCD沿AE,BF同侧折起,使得平面
平面ABFE,平面
平面BCF,得到图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/9ddce68d-b2a1-4fe9-9cf3-51bda93d81de.png?resizew=319)
(1)证明:
平面ACD;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e1a727ba332984ad857b3d25344d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82773737609e65dea3c5c67099f1b10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86338536656046e93b53672ade9a78b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d782bc4aad7cf35baa3de7b8ea73e41f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/9ddce68d-b2a1-4fe9-9cf3-51bda93d81de.png?resizew=319)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c83d44cb6b68e558952d40b2f1de15.png)
您最近一年使用:0次
解题方法
10 . 已知椭圆
:
右焦点为
,
为椭圆上异于左右顶点
,
的一点,且
面积的最大值为
.
(Ⅰ)求椭圆
的标准方程;
(Ⅱ)若直线
与直线
交于点
,线段
的中点为
,证明直线
平分
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d52429c8324350309f77e7209a5c35.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2273ae1ee99cec9c1304323bc9ebf75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d4ab4f05dbd1a4301ed0dc4c73aa75.png)
您最近一年使用:0次
2020-06-20更新
|
541次组卷
|
4卷引用:新疆乌鲁木齐地区2020届高三年级第三次质量监测理科数学试题