名校
解题方法
1 . 已知椭圆
的短轴长为
,离心率为
.
(1)求椭圆
的方程;
(2)若直线
与椭圆
相交于
,
两点(
,
不是左右顶点),且以
为直径的圆过椭圆
的左顶点
,求证:直线
过定点,并求出该定点的坐标.
![](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/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.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/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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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4卷引用:云南省弥勒市第一中学2021-2022学年高二上学期第四次月考数学试题
名校
解题方法
2 . 如图,设
,
是双曲线
的左、右焦点,过点
作渐近线的平行线交另外一条渐近线于点
,若
的面积为
,离心率满足
,则双曲线的方程为( )
![](https://img.xkw.com/dksih/QBM/2021/6/24/2754872083324928/2795406379589632/STEM/c81930ccefeb4c2ea474064011461895.png?resizew=175)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93689ff4b99182a5d30bb9383536bda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59ab85c075a09d55d69e159e4abb268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4e2759d63bd0f1a9c896c095ed4b63.png)
![](https://img.xkw.com/dksih/QBM/2021/6/24/2754872083324928/2795406379589632/STEM/c81930ccefeb4c2ea474064011461895.png?resizew=175)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7卷引用:云南省弥勒市第一中学2020-2021学年高二下学期第四次月考数学(理)试题
云南省弥勒市第一中学2020-2021学年高二下学期第四次月考数学(理)试题北师大版(2019) 选修第一册 突围者 第二章 第二节 课时2 双曲线的简单几何性质(已下线)第04讲 双曲线的简单几何性质-【帮课堂】重庆市第一中学2021-2022学年高二上学期11月月考数学试题浙江省名校协作体2022-2023学年高三下学期开学联考适应性考试数学试题(已下线)2023年天津高考数学真题变式题6-10(已下线)第八章 解析几何 专题2 双曲线方程
名校
解题方法
3 . 已知在平面四边形
中,
,
,将
沿对角线
折起,使点
到达点
的位置,当
时,三棱锥
的外接球的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e37e7962b09d2a55a3aacafedb21da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb90e62d0d1dc492c95b62d6db4602d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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4 . 已知椭圆
:
,
,
分别为椭圆长轴的左、右端点,
为直线
上异于点
的任意一点,连接
交椭圆于
点.
(1)求证:
(其中
为坐标原点)为定值;
(2)是否存在
轴上的定点
,使得以
为直径的圆恒通过
与
的交点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80b861ba40387cb2bcd04945f5a371a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9835a3c08a4f08d57e7b717a20a76af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
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3卷引用:云南省弥勒市第一中学2020-2021学年高二下学期第四次月考数学(文)试题
名校
5 . 丹麦数学家琴生是
世纪对数学分析做出卓越贡献的巨人,特别是在函数的凹凸性与不等式方面留下了很多宝贵的成果.定义:函数
在
上的导函数为
,
在
上的导函数为
,若在
上
恒成立,则称函数
是
上的“严格凸函数”,称区间
为函数
的“严格凸区间”.则下列正确命题的序号为 ____________ .
①函数
在
上为“严格凸函数”;
②函数
的“严格凸区间”为
;
③函数
在
为“严格凸函数”,则
的取值范围为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be7581dbbccda50e5d5cd18056ddea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eedbf81c9b62183b1ce85c51dd2226b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eedbf81c9b62183b1ce85c51dd2226b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eedbf81c9b62183b1ce85c51dd2226b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa4b560c48799ad63736f4fbca9b0ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eedbf81c9b62183b1ce85c51dd2226b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eedbf81c9b62183b1ce85c51dd2226b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c482e2e4631a33f5a1206901c8e9a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd2906a2efd6b93ae36e629082234630.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b26f55c7c29644dfe0277d3e2adf10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77887d864954591015412382e8b34cc5.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1807569c10a19abeab5c5587684049d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2235ed37b1bb798c2797de9019eade8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56bdb1aeda86c3a434053774bb80135.png)
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4卷引用:云南省红河州2021届高三三模数学(理)试题
云南省红河州2021届高三三模数学(理)试题四川省南充市白塔中学2022-2023学年高三上学期入学考试数学(理)试题四川省南充市白塔中学2022-2023学年高三上学期入学考试数学(文)试题(已下线)专题08 导数与函数综合压轴(选填题)-1
6 . 函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9411a8e55412678dfe6374b1a46650dd.png)
,若
的两个极值点分别为
,
,且满足
.
(1)求实数
的值;
(2)若函数
有三个零点,求证:
的所有零点的绝对值都小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9411a8e55412678dfe6374b1a46650dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31f11bc5048e6554f9afedba30fd973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1342b72ade171ff7d81d88c55cf37b04.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
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解题方法
7 . 已知函数
是定义在
的奇函数,且满足
,当
,
,则下列关于函数
叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e594ae5c001c6136ac4d4ca19b7607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f14a6618c62f7ad3776b79bbe023d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6f2251689f6525c0851fd0d39df3d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.函数![]() ![]() |
B.函数![]() ![]() |
C.函数![]() ![]() |
D.函数![]() ![]() ![]() ![]() |
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4卷引用:云南省红河州2021届高三三模数学(理)试题
云南省红河州2021届高三三模数学(理)试题(已下线)专题06 函数的概念与性质常考压轴题型-2021-2022学年高一《新题速递·数学》(人教A版2019)(已下线)专题2-2 函数性质2:“广义”奇偶性-3四川省成都市东部新区养马高级中学2022-2023学年高二下学期第一次月考理科数学试题
8 . 已知在平面直角坐标系
中,直线
的参数方程为
(
为参数),以坐标原点
为极点,
轴的非负半轴为极轴建立极坐标系,曲线
的极坐标方程为
,点
的极坐标是
.
(1)求直线
的极坐标方程及点
到直线
的距离;
(2)若直线
与曲线
交于
,
两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362f7e2d5a2938bbca944879e7ea9264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79efab82643ce554cedfa48c487fdf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8154c1e1359dbbacec5db156929bebeb.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若直线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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6卷引用:云南省红河州2021届高三三模数学(文)试题
云南省红河州2021届高三三模数学(文)试题云南省红河州2021届高三三模数学(理)试题全国Ⅰ卷2021届高三高考临考仿真冲刺卷数学(文)试题(四)(已下线)专题14 参数方程与极坐标方程-备战2022年高考数学(文)母题题源解密(全国乙卷)(已下线)第01讲 极坐标与参数方程(练)陕西省西安市部分学校2024届高三上学期普通高等学校招生全国统一考试理科数学试卷
9 . 已知函数
(1)当
时,证明:
在区间
上不存在零点;
(2)若
,试讨论函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96188b484ef24ff67153eb69967916a8.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a7792efd7f82bfa7549db4cb6ca761.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a39a792e0300794dc1f460a52f2593e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5029dfb6a8d2071481b4d4116c6ce1.png)
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10 . 已知函数
.
(1)当
时,求函数
的单调区间;
(2)若
(
为自然对数的底数),不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2c4160f363a7b1307a109c5ee77880.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7b5582e1931243dbb90b7591137f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaeea29735a7c9f1d52a8945407aee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b55e71020fa90c12cf4f613351549c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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