1 . 已知函数
.
(1)设
,证明:当
时,过原点O有且仅有一条直线与曲线
相切;
(2)若函数
有两个零点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce0da73f9c18ef1cb4e9646ff201073.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1d1feee09e10e8eceb8a5ff31ba995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
解题方法
2 . 已知椭圆
的离心率为
,左右顶点分别为A,B,G为C的上顶点,且
的面积为2.
(1)求椭圆C的方程;
(2)过点
的动直线与C交于M,N两点.证明:直线
与
的交点在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc727c642cbc2181476b7dd8eca471e.png)
(1)求椭圆C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
您最近一年使用:0次
3 . 已知双曲线
的左、右焦点分别为
,
,点P在直线
上.当
取最大值时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e1aa8ad8272eac52b680547e47bf00.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6cf8bc908b192921416bb2d958ed539.png)
![](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/19cba91dc2ff8cd1d5771f06f66f9d48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e1aa8ad8272eac52b680547e47bf00.png)
您最近一年使用:0次
名校
解题方法
4 . 已知直线
轴,垂足为x轴负半轴上的点E,点E关于原点O的对称点为F,且
,直线
,垂足为A,线段AF的垂直平分线与直线
交于点B,记点B的轨迹为曲线C.
(1)求曲线C的方程;
(2)已知点
,不过点P的直线l与曲线C交于M,N两点,以线段MN为直径的圆恒过点P,点P关于x轴的对称点为Q,若
的面积是
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dd42188ae3b66affd240183dd395c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accb5ad69bc5a1cfa04bb429a91f1c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(1)求曲线C的方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497911bc462170183e81d95bd509b70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44eff0c9eaadd16c8afad11bacb053f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41e62f89e235395f1ab253688fc5b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-08-03更新
|
548次组卷
|
7卷引用:四川省南江中学2023届高三下学期五月适应性考试(一)文科数学试题
四川省南江中学2023届高三下学期五月适应性考试(一)文科数学试题湖南省部分学校2023届高三下学期5月联数学试题贵州省2023届高三多校联考数学(文)试题湖北省武汉第六中学2024届高三上学期第一次月考数学试题河南省驻马店市2023届高三第二次联考文科数学试题河南省创新发展联盟2023届高三高考仿真模拟预测文科数学试题(已下线)专题08 抛物线的压轴题(5类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)
名校
5 . 已知函数
.
(1)求曲线
在
处的切线方程;
(2)若函数
,不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a3f0df954a6a1e535463417b6632c5.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7703b3476f3eb983031474ad1fec698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70202ea6849246dd6d00e38ddf96dc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-05-21更新
|
265次组卷
|
4卷引用:四川省南江中学2023届高三下学期五月适应性考试(一)文科数学试题
名校
解题方法
6 . 已知直线
轴,垂足为
轴负半轴上的点
,点
关于坐标原点
的对称点为
,且
,直线
,垂足为
,线段
的垂直平分线与直线
交于点
.记点
的轨迹为曲线
.
(1)求曲线
的方程.
(2)已知点
,不过点
的直线
与曲线
交于M,N两点,以线段
为直径的圆恒过点
,试问直线
是否过定点?若是,求出该定点坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dd42188ae3b66affd240183dd395c3.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accb5ad69bc5a1cfa04bb429a91f1c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497911bc462170183e81d95bd509b70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-05-20更新
|
679次组卷
|
4卷引用:四川省南江中学2023届高三下学期五月适应性考试(一)理科数学试题
名校
7 . 已知函数
,
.
(1)讨论
的单调性;
(2)已知
是
的导函数,若对任意的
,都有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53196b402e11e898e450c7820b1b9515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb413c37f170adfa576394afa3d29d7.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e5f867761781897f53860a579b6086c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-05-19更新
|
566次组卷
|
4卷引用:四川省南江中学2023届高三下学期五月适应性考试(一)理科数学试题
名校
解题方法
8 . 已知双曲线
的左、右焦点分别为
,
,P是C在第一象限上的一点,且直线
的斜率为
,点B为
的内心,直线PB交x轴于点A,且
,则双曲线C的渐近线方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](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/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640140654b6ea480d761858fa00625cd.png)
您最近一年使用:0次
2023-04-18更新
|
692次组卷
|
4卷引用:四川省巴中市南江县南江中学2023届高三二模数学(理)试题
9 . 已知椭圆
的左、右焦点分别为
,
,左顶点为
,离心率为
,经过
的直线交椭圆于
两点,
的周长为8.
(1)求椭圆
的方程;
(2)过直线
上一点P作椭圆C的两条切线,切点分别为
,
①证明:直线
过定点;
②求
的最大值.
备注:若点
在椭圆C:
上,则椭圆C在点
处的切线方程为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8376a8a3dd42eaa0558501a3e2a2bdb4.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39b4ab8209e56bf6ece460b90c3f1b9.png)
备注:若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9656735f55e5de465e5667ba578d4e.png)
您最近一年使用:0次
10 . 设函数
,
.
(1)当
时,设
,求函数
的单调区间;
(2)若函数
有两个零点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b31cbbe4d33302cf2ec6b0dbd5d437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffdd3fc86fae4c7ace0e9f6b7c8b6788.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d326596f3ec9ce391cd16ab3c213eaab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次