名校
1 . 已知函数
.
(1)当
时,求证:
;
(2)当
时,若不等式
恒成立,求实数
的取值范围;
(3)若
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41f0a059d02f88033d4c46fbe648ba2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bc1807f5f5784e75c4e5e6df17f3ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e2d7a7b5ef6de479ac02b04965245d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a154aa77357cb73cbcd37275d873a324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e2d7a7b5ef6de479ac02b04965245d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d9c89d2cd1fb46b1e71ad10227c098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a375205425cf8092535bcc485646fdc3.png)
您最近一年使用:0次
2019-03-30更新
|
1687次组卷
|
8卷引用:山东省淄博实验中学2018-2019学年高三寒假学习效果检测(开学考试)数学(理科)试题
解题方法
2 . 如图,P是直线
上一动点,以P为圆心的圆Γ经定点B(1,0),直线l是圆Γ在点B处的切线,过
作圆Γ的两条切线分别与l交于E,F两点.
(1) 求证:
为定值
(2)设直线l交直线
于点Q,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0038fefa3631a3b3064033ae6606366b.png)
![](https://img.xkw.com/dksih/QBM/2017/8/8/1747568471793664/1747951295881216/STEM/e791b8c1073148c7978576ae0766b6e5.png?resizew=227)
(1) 求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2843730ec1403be97a27545eca962fe6.png)
(2)设直线l交直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e49a7a701fbc3274234126cd30b127.png)
您最近一年使用:0次
2017-08-08更新
|
1160次组卷
|
2卷引用:安徽省定远县育才学校2017-2018学年高二下学期开学调研考试数学(理)试题
3 . 在平面直角坐标系 xoy 中,离心率为
的椭圆C:
(a>b>0)的左顶点为A,且A到右准线的距离为6,点P、Q是椭圆C上的两个动点.
![](https://img.xkw.com/dksih/QBM/2016/5/19/1572642452848640/1572642458624000/STEM/8b42c05c959a4c2ba5984b8fa0e87d95.png)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)如图,当P、O、Q共线时,直线PA,QA分别与y轴交于M,N两点,求证:
为定值;
(Ⅲ)设直线AP,AQ的斜率分别为k1,k2,当k1
k2= -1时,证明直线PQ经过定点R.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/2016/5/19/1572642452848640/1572642458624000/STEM/8ec380e9eba84f289075cbc9a5e19fcb.png)
![](https://img.xkw.com/dksih/QBM/2016/5/19/1572642452848640/1572642458624000/STEM/8b42c05c959a4c2ba5984b8fa0e87d95.png)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)如图,当P、O、Q共线时,直线PA,QA分别与y轴交于M,N两点,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ae3ec5b77ae970b379c2f5e8da4c2.png)
(Ⅲ)设直线AP,AQ的斜率分别为k1,k2,当k1
![](https://img.xkw.com/dksih/QBM/2016/5/19/1572642452848640/1572642458624000/STEM/810b96b489ff4279a2dc27b15fc6691c.png)
您最近一年使用:0次
2014·北京石景山·一模
名校
解题方法
4 . 给定椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
,称圆心在原点
,半径为
的圆是椭圆
的“准圆”.若椭圆
的一个焦点为
,其短轴上的一个端点到
的距离为
.
的方程和其“准圆”方程;
(2)点
是椭圆
的“准圆”上的动点,过点
作椭圆的切线
交“准圆”于点
.
①当点
为“准圆”与
轴正半轴的交点时,求直线
的方程并证明
;
②求证:线段
的长为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da001dad7941e6c9858637d7b62cec59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c86bc114a286413e3933352392080a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
②求证:线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2016-12-02更新
|
1800次组卷
|
8卷引用:北京一零一中学2023届高三下学期开学考数学试题
北京一零一中学2023届高三下学期开学考数学试题(已下线)2014届北京市石景山区高三一模理科数学试卷(已下线)2014届甘肃省兰州一中高考模拟四理科数学试卷(已下线)2014届甘肃省兰州一中高考模拟四文科数学试卷2015-2016学年河北省石家庄一中高二下期中文科数学试卷河北省衡水中学2017届高三高考猜题卷(一)数学(理)试题山西省大同市第一中学2019-2020学年高三下学期模拟(六)数学(理)试题(已下线)微专题07 直线与圆锥曲线的相切问题
5 . 已知椭圆
的上顶点为
,右焦点为
,原点
到直线
的距离为
的面积为1.
(1)求椭圆
的方程;
(2)过点
的直线
与
交于
两点,过点
作
轴于点
,过点
作
轴于点
与
交于点
.
①求证:点
在定直线上,
②求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767a75d8d8add0ffa3db20e77797df31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8452ffb321d5cf3887a129757b78e9.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea91b1fb8690c09739e2981735f1919f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecde35e9255cb7922a86536b05f4a302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c217dadaca86779f03a2760377b6be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d8e33929752b1cb4dd36ee9b98b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
您最近一年使用:0次
6 . 基本不等式:对于2个正数
,它们的算术平均数不小于它们的几何平均数,即
,当且仅当
时,等号成立.可以推广到一般的情形:对于
个正数
,它们的算术平均数不小于它们的几何平均数,
.当且仅当
时,等号成立.若无穷正项数列
同时满足下列两个性质:①
;②
为单调数列,则称数列
具有性质
.
(1)若
;求数列
的最小项;
(2)若数列
的前
项和为
,判断数列
是否具有性质
,并说明理由;
(3)若
,求证:数列
具有性质
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140564fb2e11f8411e353d2fa73fbee9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b2fb1017d5dfe3a300de3e14a71b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efff8ec14cb242e793afab4468bf2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2617515e5ce81b3f5d9f4e806b21b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6879960be91ea52297d587e9a014f54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17fac66473a039bdb47c2a248b0f4854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9bb1963d176a00c82828c93ca0e2c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4247739746b8ddf1403541047e8b5580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
7 . 已知函数
,其中
.
(1)讨论
的单调性;
(2)若
,求证:
在定义域内有两个不同的零点;
(3)若
恒成立,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4a821c91ff2397cf62f19c319b4b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5d4d37afd15e1f3742b0fb0ef5daca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6f2ac1f581a415cac5235661ed1981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
8 . 设点
是椭圆
上任意一点,过点
作椭圆的切线,与椭圆
交于
两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ace6602b-ed9b-4579-a1ec-98d61a6294b3.png?resizew=155)
(1)求证:
;
(2)
的面积是否为定值?若是,求出这个定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e91e565e14d96a20169db44fcde58a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ace6602b-ed9b-4579-a1ec-98d61a6294b3.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b0bec6e780130fbed900fdb153555d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2024-02-05更新
|
1469次组卷
|
6卷引用:四川省成都市第七中学2024届高三下学期入学考试数学(文)试题
9 . 已知点
在抛物线
的准线上,过点
作直线
与抛物线
交于
两点,斜率为2的直线与抛物线交于
两点.
(1)求抛物线
的标准方程;
(2)① 求证:直线
过定点
;
② 若
的面积为
,且满足
,求直线
斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc2de9df8bce6139613bb86322db0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e478787ebfeb68a5a7594dbd9eecd4.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)① 求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
② 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c8bef41fa6778e5eb57e2f19ea48f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-01-27更新
|
264次组卷
|
3卷引用:江苏省徐州市沛县第二中学2024届高三下学期期初测试数学试题
江苏省徐州市沛县第二中学2024届高三下学期期初测试数学试题湖北省武汉外国语学校2023-2024学年高二上学期期末考试数学试题(已下线)2.4.2 抛物线的性质(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
10 . 已知函数
.
(1)讨论
的单调性;
(2)设
,求证:当
时,
恰有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae648c38a4f55310db639082bfcca39.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6b456391f0ee447887b2091344205f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
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4卷引用:四川省绵阳市南山中学2024届高三下学期入学考试数学(理)试题
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