解题方法
1 . 已知椭圆
的左、右顶点分别是
,椭圆
的焦距是2,
(异于
)是椭圆
上的动点,直线
与
的斜率之积为
.
(1)求椭圆
的标准方程;
(2)
分别是椭圆
的左、右焦点,
是
内切圆的圆心,试问平面上是否存在定点
,使得
为定值?若存在,求出该定值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](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/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350a38070bdc27207946be17d5f70223.png)
您最近一年使用:0次
名校
解题方法
2 . 已知
,
分别是椭圆
:
(
)的左、右顶点,
为
的上顶点,
是
上在第一象限的点,
,直线
,
的斜率分别为
,
,且
.
(1)求
的方程;
(2)直线
与
交于点
,
与
轴交于点
,求
的取值范围.
![](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/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b8ff98fbd2376ba4214f34026b01a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eac9ba606fb477550aa62db7bfa0ac4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdbd4e4d9389c775a42e0ac36579029.png)
您最近一年使用:0次
2024-03-21更新
|
615次组卷
|
2卷引用:河南省新乡市2024届高三第二次模拟考试数学试题
名校
3 . 已知椭圆
与双曲线
的焦距之比为
.
(1)求椭圆
和双曲线
的离心率;
(2)设双曲线
的右焦点为F,过F作
轴交双曲线
于点P(P在第一象限),A,B分别为椭圆
的左、右顶点,
与椭圆
交于另一点Q,O为坐标原点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e8ecb41c1e7e0cea771f75ccf1b6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb7c47e3b286437d8e6ee8b7ec4f003.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932b5ed149ea885cfd5353ff2e6ceac2.png)
您最近一年使用:0次
2024-01-25更新
|
959次组卷
|
8卷引用:河南省新乡市2023-2024学年高二上学期1月期末测试数学试题
名校
4 . 设
,
,
,函数
,
.
(1)讨论函数
的单调性;
(2)若
时,函数
有三个零点
,
,
,其中
,试比较
与
的大小关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5331eda67df4c98b3e0dc31a46d381ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a64103561364ac4c9460a72c9e154bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ded5b08362289af5696ca4cd1a6f36d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f291d4a407115b7a83c2621489f5df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0a92b7176bb67c18ca5f043eba98b5.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce4cea6c8b740796100f76320ae9806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10db649c154fc538026c0779325b91f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd39b02127b0b5085c2dcc7205f5a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f0f405ce844313744d1ccfd222c3dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec733ccf28e47e673cb7d4a73be08a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b546dfbc651d94c624d57b25bcee6331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e20d46ff63add7948a6a26c7baa9ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
您最近一年使用:0次
2024-01-12更新
|
433次组卷
|
10卷引用:河南省新乡市2022-2023学年高二下学期期末数学试题
5 . 已知函数
.
(1)当
时,讨论
在
上的单调性;
(2)已知
是
的两个零点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c35a3bcb53c7913523de568b46d8021.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111870a9ef48f1bb2797ae8f1825a8f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd5072eda34e5a10e2c9c4805380ade.png)
您最近一年使用:0次
解题方法
6 . 已知函数
的定义域为
,且满足对任意
,
,有
.
(1)求
,
的值;
(2)判断函数
的奇偶性并证明你的结论;
(3)当
时,
,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d09dcbc6f4e0317fabb545af7d7c7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23478a1fcd7ba7a2a7adc61f20b1d6b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32822a106d217ffdec43557a236f786.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93aaa61ae9d067e28f9c05d13740e22.png)
您最近一年使用:0次
2023-11-28更新
|
289次组卷
|
4卷引用:河南省新乡市第十二中学2023-2024学年高一下学期开学考试数学试卷
河南省新乡市第十二中学2023-2024学年高一下学期开学考试数学试卷河北省沧州市2023-2024学年高一上学期11月期中考试数学试题河北省石家庄市第二十八中学2023-2024学年高一上学期期中数学试题(已下线)专题04 函数的性质与应用2-期末复习重难培优与单元检测(人教A版2019)
名校
7 . 已知函数
和
有相同的最小值,(e为自然对数的底数,且
)
(1)求m;
(2)证明:存在直线
与函数
,
恰好共有三个不同的交点;
(3)若(2)中三个交点的横坐标分别为
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0166bbd15fa298c0d6a90a639108f4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6db457ee2d041b542c3eeff31d94cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)求m;
(2)证明:存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79f45b5880c72a349500da9d8e118d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)若(2)中三个交点的横坐标分别为
![](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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c06ceee2b1e227de025476eee95672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5b965b3f27889e139013aa8c8f8fe3.png)
您最近一年使用:0次
2023-11-10更新
|
363次组卷
|
4卷引用:河南省新乡市原阳县第一高级中学2023-2024学年高一上学期12月月考数学试题
名校
8 . 已知函数
,
.
(1)判断是否存在x,使得
,若存在,求出x的值;若不存在,请说明理由;
(2)讨论
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5cdd121d6baa6aaf78ec5c039b23160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b66150793c738ead964a3ea4446a87.png)
(1)判断是否存在x,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3622cfa680fa35702bc840d8aa80f593.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2023-11-03更新
|
443次组卷
|
4卷引用:河南省新乡市普高联考2023-2024学年高三上学期测评(三)数学试题
河南省新乡市普高联考2023-2024学年高三上学期测评(三)数学试题江苏省徐州市普高联考(求实高中等)2023-2024学年高三上学期测评(三)数学试题重庆市永川萱花中学校2023-2024学年高三上学期期中考试数学试题(已下线)第3讲:利用导数研究不等式恒成立、能成立问题【练】 高三清北学霸150分晋级必备
名校
解题方法
9 . 已知函数
.
(1)若
,
,求实数a的取值范围;
(2)设
,
是函数
的两个极值点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b26e9c2bd96441e1db6799681ca9b0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
(2)设
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b78ccc2ef147d41adc50cb7fa57786.png)
您最近一年使用:0次
2023-09-01更新
|
277次组卷
|
2卷引用:河南省新乡市第二中学2024届高三上学期1月测试数学试题
名校
解题方法
10 . 已知函数
.
(1)若函数
在区间
上为增函数,求
的取值范围;
(2)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01e15dad74c8745b8ce5a326215e8b7.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cee2f443936271cf621236882776d7c.png)
您最近一年使用:0次
2023-07-24更新
|
553次组卷
|
4卷引用:河南省新乡市第一中学2024届高三上学期一轮复习11月考试数学试题