1 . 已知椭圆
的离心率为
,长轴长为4.
(1)求椭圆C的标准方程;
(2)O为坐标原点,过点
且斜率不为零的直线与椭圆C交于E,F两点,试问:在x轴上是否存在一个定点T,使得
.若存在,求出定点T的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆C的标准方程;
(2)O为坐标原点,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa77e019204efd90ea6e733420eceef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a8b03f29c26f7e7d9f1e6e21e079bb.png)
您最近一年使用:0次
2024-05-28更新
|
310次组卷
|
2卷引用:广西2024届高中毕业班上学期9月摸底检测数学试题
2 . 已知函数
.
(1)若
在
处取得极值,求
的极值;
(2)讨论
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b7781db4cd08d80b1173906f65cd3c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在四棱锥
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
为
的中点,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
平面
,
(1)证明:
;
(2)若
平面
,点
在四棱锥
的底面内,且在以
为焦点,并满足
的椭圆弧上.若二面角
的余弦值为
,求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1caf930db3fed80bdba0ee52bc8a1b24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.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/e7b7c83470489253394bd288d7c920df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/a9e26599-26d2-4bfb-8dde-2f1f9619f792.png?resizew=178)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a69df64811eb0866c84207f24dfae99.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f8a6b71a28aa8beef35e1cd77c177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9571f313b799a9654ac131c335807386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3ec0acc744c89cc5e7bb63c32a8714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e468f168f3657d84d44be5eb89a62d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
4 . 已知椭圆
的长轴长为
,且其离心率小于
为椭圆
上一点,
分别为椭圆
的左、右焦点,
的面积的最大值为
,
(1)求椭圆
的标准方程;
(2)
为椭圆
的上,下顶点,过点
且斜率为
的直线与椭圆
交于
两点,过点
且与
平行的直线与直线
的交点为
,设直线
所成角为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2bc9325e8dcd6586b5bd19b2d5be1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278b6daa22ae6eacde264a76d9c64b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b27aee52676f4237adac068fe745fde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be82ace0fc6139bbffcebba1160f1fe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc24d605ad707ad0e76059d8a31f50d3.png)
您最近一年使用:0次
5 . 已知数列
的前
项和、前
项和、前
项和分别为
、
、
,则“
为等比数列”的一个必要条件为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f41be870e84c819362787849770519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
6 . 已知函数
的定义域为
,且
,若
,则( )
![](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/09a929628a481aaa14fdbcda369e7399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709c3563b82d595c9f25e77ec0084f63.png)
A.![]() | B.![]() |
C.函数![]() | D.函数![]() |
您最近一年使用:0次
2024-01-19更新
|
7367次组卷
|
13卷引用:广西南宁市第三十六中学2024届高三下学期适应性训练数学试题
广西南宁市第三十六中学2024届高三下学期适应性训练数学试题2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题11-152024年九省联考试卷分析及真题鉴赏(已下线)函数的图象与性质(已下线)新题型01 新高考新结构二十一大考点汇总-2辽宁省锦州市北镇市满族高级中学2024届高三下学期第一次月考数学试题(已下线)专题02 函数图象及性质(分层练)(四大题型+11道精选真题)(已下线)专题9 解决抽象函数问题(已下线)专题6 学科素养与综合问题(多选题11)山东省临沂第一中学2023-2024学年高一上学期期末模拟数学试题山东省临沂第十八中学2023-2024学年高一下学期2月收心考试数学试题福建省厦门双十中学2023-2024学年高二下学期开学考试数学试题
名校
7 . 已知函数
,
(1)当
时,求
在区间
上的值域;
(2)若
有两个不同的零点
,求
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e9f45f86ee4cac88d16435393c7cec.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/1e7eccdc19dbe2b4c7a30878c054e8c7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29909a4fdb8764b59f28bb63ce8da9db.png)
您最近一年使用:0次
2024-01-15更新
|
463次组卷
|
3卷引用:广西柳州市高级中学2024届高三上学期12月月考数学试题
8 . 假设
市四月的天气情况有晴天,雨天,阴天三种,第二天的天气情况只取决于前一天的天气情况,与再之前的天气无关.若前一天为晴天,则第二天下雨的概率为
,阴天的概率为
;若前一天为下雨,则第二天晴天的概率为
,阴天的概率为
;若前一天为阴天,则第二天晴天的概率为
,下雨的概率为
;已知
市4月第1天的天气情况为下雨.
(1)求
市4月第3天的天气情况为晴天的概率;
(2)记
为
市四月第
天的天气情况为晴天的概率,
(i)求出
的通项公式;
(ii)
市某花卉种植基地计划在四月根据天气情况种植向日葵,为了更好地促进向日葵种子的发芽和生长,要求提前3天对种子进行特殊处理,并尽可能地选择在晴天种植.如果你是该花卉种植基地的气象顾问,根据上述计算结果,请你对该基地的种植计划提出建议.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ee3c61d2298e75fc4f1643f8ebc2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a53ec845256c1f577acf5472a925cb9.png)
(i)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
您最近一年使用:0次
名校
解题方法
9 . 已知
是等差数列
的前
项和,满足
,设
,数列
的前
项和为
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d308242e322289b950c25f9637da73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230ae9538a1b0ec62c3491cbce25df8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
A.![]() |
B.使得![]() ![]() |
C.![]() |
D.当![]() ![]() |
您最近一年使用:0次
解题方法
10 . 已知椭圆
的左、右焦点分别是
,且椭圆过点
.
(1)求椭圆
的方程;
(2)过
的左焦点
作弦
,这两条弦的中点分别为
,若
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5439f5ff9bd5deec0f0ef35c6f605b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af292f60c635d2bb4c38379c6bd04ac5.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38858b26bf0219e5f0cd95299a1ae153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0be401c4e805b265e443e22ebc9dfa85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2024-01-10更新
|
213次组卷
|
2卷引用:广西壮族自治区名校2023届高三上学期11月联考数学(理)试题