1 . 已知动圆
经过定点
,且与圆
:
内切.
(1)求动圆圆心
的轨迹
的方程;
(2)设轨迹
与
轴从左到右的交点为
,
,点
为轨迹
上异于
,
的动点,设
交直线
于点
,连接
交轨迹
于点
,直线
,
的斜率分别为
,
.
①求证:
为定值;
②证明:直线
经过
轴上的定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866502435d9ea08c6d3a5e304a8986c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8387b687579c4d5152175c9d19e24232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9811dd726ed27d28ad5a8e83fbb20ed6.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/dad2a36927223bd70f426ba06aea4b45.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/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef79861421b414b455a090a3ef04fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b51a4949896526cfc3c076ea8dec8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128147bd4834566a78b4e9d2a3b2139c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4a51e6728d354cc1c3d32e2d4368d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729d727db2181aca4e8a6455d10cfe28.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6b1769274eee3ce2896cb3513d50f8.png)
②证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024-01-11更新
|
630次组卷
|
11卷引用:四川省泸州市泸县第一中学2024届高三上学期期末数学(理)试题
名校
2 . 已知函数
.
(1)求证:存在唯一的
,使得曲线
在点
处的切线的斜率为
;
(2)比较
与
的大小,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91736d59da6c5a18c2114f2bbd61e245.png)
(1)求证:存在唯一的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155c7f573e898da225390202da1767e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e679eeda70ca6df048ed7e5991229c.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9b6d24584aa74e9fc5d80281ec7fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b708034aa1e680d6b14ce2133650a85.png)
您最近一年使用:0次
2021-01-29更新
|
191次组卷
|
2卷引用:四川省成都市青羊区石室中学2020-2021学年高三上学期期末数学试题
3 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
(1)证明:
;
(2)设
为正数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e778f95c72fec00bfbbc63e6dfd0c460.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da2f7eb5dbdfc4da06cbf22555502fb.png)
您最近一年使用:0次
2018-01-07更新
|
307次组卷
|
5卷引用:四川省成都市双流区双流棠湖中学2019-2020学年高三上学期期末数学(理)试题
四川省成都市双流区双流棠湖中学2019-2020学年高三上学期期末数学(理)试题2020届四川省成都市双流区棠湖中学高三上学期期末考试数学(文)试题辽宁省沈阳市交联体2018届高三上学期期中考试文数试题(已下线)黄金30题系列 高三年级数学(文) 大题易丢分(已下线)江西省九所重点中学2023届高三第二次联考联合考试数学(文)试题变式题21-23
解题方法
4 . 几何体
中,
是正方形,
是直角梯形,
,
,
,
,
,
为
的中点.
平面
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
.
(2)求几何体
的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca9eb9126c7053574c62b897582ad49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75d2e5e5ec3caea31e3928183eebbc2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb52f9b226b1db3f6f9f055948bd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e343510d82161bb1da2f17403f5d1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50942a23ce671c3af03baf4ee1219a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613dedf2d90e58591b7ac4a250ac7b5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbef3d7ab3df5cfeb82ca8e34379dbf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb26696808cd8878f19ae3d69484b042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(2)求几何体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca9eb9126c7053574c62b897582ad49.png)
您最近一年使用:0次
解题方法
5 . 已知椭圆
的焦距为2,经过点
.
(1)求椭圆
的标准方程.
(2)椭圆
的左顶点为
,过其右焦点
且斜率不为0的直线
交椭圆
于
两点,记直线
的斜率分别为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe8530b8e246a9a5ec9fe3b9c347d5a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
您最近一年使用:0次
解题方法
6 . 已知
.
(1)若
,证明
与
中至少有一个小于0;
(2)若
均为正数,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c175e7e4f89080b5c19fa3fbcfc47b56.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2584d4e78881413d8ddd1ec84011db2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9a692e9a18ebf339be5e7c25e2aac3.png)
您最近一年使用:0次
2024-02-22更新
|
89次组卷
|
2卷引用:四川省部分名校2023-2024学年高三上学期期末联合考试文科数学试题
7 . 如图,在四棱锥
中,底面
为矩形,平面
平面
,
是边长为2的正三角形,延长
至点
,使得
为线段
的中点.
(1)证明:
平面
.
(2)若
,求四棱锥
的体积.
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/895598f2-9124-4903-a726-c6aef73f67a0.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd7c2767c106faf27d6a97ebc8e739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
您最近一年使用:0次
2024-02-17更新
|
448次组卷
|
4卷引用:四川省部分名校2023-2024学年高三上学期期末联合考试文科数学试题
四川省部分名校2023-2024学年高三上学期期末联合考试文科数学试题(已下线)第07讲 空间直线﹑平面的垂直(二)-《知识解读·题型专练》13.3 空间图形的表面积和体积(1)-【帮课堂】(苏教版2019必修第二册)(已下线)13.3 空间图形的表面积和体积(2)-【帮课堂】(苏教版2019必修第二册)
8 . 如图,在四棱锥
中,底面
为直角梯形,
,
,侧面
面
,
,
,
为
的中点.
面
;
(2)若
的大小为
,求四棱锥
的体积.
![](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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b72c6d2ae4924f930c437542b3356a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59bafaec1cbb31d644a0df6bbd4fe4f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,在四棱锥
中,底面
为直角梯形,
,
,侧面
面
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/8ceef9d8-8a99-41e6-b151-7939bde3f9c9.png?resizew=163)
(1)求证:面
面
;
(2)若二面角
的大小为
,求
与面
所成角的正弦值.
![](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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b72c6d2ae4924f930c437542b3356a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.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/2024/2/15/8ceef9d8-8a99-41e6-b151-7939bde3f9c9.png?resizew=163)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c911b404bbb8f8d5f1470585fa31ad97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在几何体
中,
平面
为
上的点,
是
的中点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/a164e176-08b2-43d1-8c35-b6a414a987eb.png?resizew=157)
(1)若
,求证:
平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd654221ab95fe241d9e0202443f2609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d62dc584a772c35e4843396151d77f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af9b8659fc0f283a3a8ec62d6e30bff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/a164e176-08b2-43d1-8c35-b6a414a987eb.png?resizew=157)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8e8f8b75e657565fe628d869b0bde3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d53d5c96de34fcf95794e51c2761b671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f713da7dce54965bbef060ad2b507e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
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