名校
解题方法
1 . 已知椭圆
的离心率为
,椭圆的一个顶点与两个焦点构成的三角形面积为2. 已知直线
与椭圆C交于A,B两点,且与x轴,y轴交于M,N两点.
(1)求椭圆C的标准方程;
(2)若
,求k的值;
(3)若点Q的坐标为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53112fe62f62d23cc1f982099f0b0acc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/7a11261c-c492-4346-aef5-d3884c920ed8.png?resizew=175)
(1)求椭圆C的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5df68b7d1fd358239f30ab81fd6014.png)
(3)若点Q的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174ce6907c1d4b19c59ac3a35188a3a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d871b0b46194d7300950e04f085533d2.png)
您最近一年使用:0次
2023-12-25更新
|
1301次组卷
|
10卷引用:上海交通大学附属中学2023届高三下学期期中数学试题
上海交通大学附属中学2023届高三下学期期中数学试题上海市浦东新区进才中学2023-2024学年高二上学期12月月考数学试题上海市新川中学2023-2024学年高二上学期期末数学试题上海市嘉定区第二中学2023-2024学年高二下学期3月月考数学试题【全国市级联考】天津市部分区2018年高三质量调查(二)数学(文)试题(已下线)专题44 盘点圆锥曲线中的定值问题——备战2022年高考数学二轮复习常考点专题突破(已下线)重难点突破16 圆锥曲线中的定点、定值问题 (十大题型)-1广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(一)宁夏银川市宁夏育才中学2023-2024学年高三上学期月考五数学(理科)试卷广西壮族自治区百色市德保县德保高中2023-2024学年高二下学期3月月考数学试题
名校
解题方法
2 . 已知椭圆
:
中,A为
的上顶点,P为
上异于上、下顶点的动点,
为x轴上的动点.
(1)若
,求点P的纵坐标;
(2)设
,若
是直角三角形,求
的值;
(3)若
,是否存在以AM,AP为邻边的平行四边形MAPQ,使得点Q在
上?若存在,求出此时点P的纵坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f20514de7d0eda255ce62f94fdd0bc7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140a5a69235a6e398c894955cc1bb1b5.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cccdb7fef301425d53500da01970184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/784b26de6134b6d3f5a81e2882a7d7f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96554444f1c1797a8c47149d65705092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
您最近一年使用:0次
2023-12-20更新
|
459次组卷
|
2卷引用:上海市虹口区上海外国语大学附属外国语学校2024届高三上学期期中数学试题
3 . 已知定义域为
的函数
.当
时,若
是严格增函数,则称
是一个“
函数”.
(1)判断函数
是否为
函数;
(2)是否存在实数
,使得函数
是
函数?若存在,求实数
的取值范围;否则,证明你的结论;
(3)已知
,其中
,证明:若
是
上的严格增函数,则对任意
,
都是
函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49439065fd967d4bd12365cf291b8d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5707b77c17eca36e53457fdbc7912ae.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f782e1eb033fdfa32dac8edfb8b57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59df0f69cdcb8bbd1e7369d3b730ab6.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a5d18c6a10ade2da30034fa84ddd4a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7afbc0eb2f8879cbf27d3cb87068de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae036504cdbfb1f2e2bf9ed5fe2b2968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9dd3d2b2e6a989d52301fecc39eb74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77339863130aaa1db8c2f851604b100b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b00438433719b82971f9fe309e04b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7f440f809129f5f0fdb8a82877e619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef5f56f08fd326e87c0b607a5c89ba7.png)
您最近一年使用:0次
解题方法
4 . 设
.
(1)求证:直线
与曲线
相切;
(2)设点P在曲线
上,点Q在直线
上,求
的最小值;
(3)若正实数a,b满足:对于任意
,都有
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)设点P在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
(3)若正实数a,b满足:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380198f4a7641d6585d8e68056abf6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
您最近一年使用:0次
名校
解题方法
5 . 平面上,直线
和
相交于点
,它们的夹角为
.已知动点
到直线
与
的距离之积为定值
,动点
的轨迹记为曲线
.我们以
为坐标原点,以直线
与
夹角的平分线为
轴,建立直角坐标系,如图.
(1)求曲线
的方程;
(2)当
,
时,直线
与曲线
顺次交于A、B、C、D四点,求证:
;
(3)当
,
时,是否存在直线
与曲线
只有A、B、C三个不同公共点(点B在线段
上),使得
?若存在,求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267572d2dff2dc38cf9251b7f33a3e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9ecfc9d5e1ff0c363f93e258e4679b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/20/d13bd123-b121-4911-9e9f-fed6d236674d.png?resizew=303)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905dd10639c9fef5ef8d66a124756140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea53167e60459eac1b64c734a3f1b48b.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c990597f83d248eb36d57d86508c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e98a8e304d4e4654d6f538e8b01039b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d514783895850481ebcb10d8b8354884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
6 . 已知双曲线
的离心率为
.
(1)若
,且双曲线
经过点
,求双曲线
的方程;
(2)若
,双曲线
的左、右焦点分别为
,焦点到双曲线
的渐近线的距离为
,点
在第一象限且在双曲线
上,若
=8,求
的值;
(3)设圆
,
. 若动直线
与圆
相切,且
与双曲线
交于
时,总有
,求双曲线
离心率
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c4088276acdbede4781b2ebc466366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5641df2cf6ae774d06733a2f73172a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937dbb96343b8a9e52718e785e9eda43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0c9cfe312930e6277eb0a47c461eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea48b907940af48c3702a328de32376b.png)
(3)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ff7cd20d1c54ce78d45429e242155f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f788fb0059b7356dc6c7811f46057e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
您最近一年使用:0次
2023-12-13更新
|
428次组卷
|
2卷引用:上海市青浦区朱家角中学2023-2024学年高二下学期期中考试数学试题
名校
7 . 设函数
与
的定义域均为
,若存在
,满足
且
,则称函数
与
“局部趋同”.
(1)判断函数
与
是否“局部趋同”,并说明理由;
(2)已知函数
.求证:对任意的正数
,都存在正数
,使得函数
与
“局部趋同”;
(3)对于给定的实数
,若存在实数
,使得函数
与
“局部趋同”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3102c0a2f53b80f9dddbf9352537e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099adf32792e7334032a80084e0cb584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0635e4216fd981fe2fafe03f423e4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2615d97b6220461ab6d33a2a77d023e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b70dafc06f46f845f5f9f5d358ffac0.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba3790e7c18ab2ccf837eada459a0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7172f1fed97ccac6aa8f6c5b992a79c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f095d2a88a647aa69a6e9e84899a408.png)
(3)对于给定的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7f03861a1d6a0b3306862f4c70161d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b68ab7272a08f28e6c76c962568c3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-12-06更新
|
284次组卷
|
2卷引用:上海市黄浦区2024届高三上学期期中调研测试(一模)数学试题
名校
解题方法
8 . 若函数
在
上是严格单调函数,则实数a的取值范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c770d5bae90a683ceb617d351d0c49db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df239c7f7e42d662e3ffdf03a55a6156.png)
您最近一年使用:0次
2023-11-26更新
|
932次组卷
|
5卷引用:上海市华东师范大学附属周浦中学2023-2024学年高三上学期期中考试数学试题
上海市华东师范大学附属周浦中学2023-2024学年高三上学期期中考试数学试题上海市向明中学2023-2024学年高二下学期期中考试数学试题2024届上海市长宁区高考一模数学试题(已下线)第五章 导数及其应用(知识归纳+题型突破)(2)(已下线)高二下学期第一次月考填空题压轴题十四大题型专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)
9 . 设函数
.
(1)当
时,求
在点
处的切线方程;
(2)当
时,求
的最大值;
(3)若
存在两个零点
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afba74ea3050996d4e625547d9f4aee.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff32d26c8d44f5fb4813a19c1030a9f5.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.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/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次