1 . 已知抛物线
经过点
.
(1)求抛物线
的方程;
(2)动直线
与抛物线
交于不同的两点
,
,
是抛物线上异于
,
的一点,记
,
的斜率分别为
,
,
为非零的常数.
从下面①②③中选取两个作为条件,证明另外一个成立:
①
点坐标为
;②
;③直线
经过点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)动直线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/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/df64046e91b047037f19e4032e3b6de3.png)
从下面①②③中选取两个作为条件,证明另外一个成立:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ca6a90ebd1486668a78b938e003e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c04c1b0a7ba45962889b559b20d484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6ce0e134669fcdf7329c01eae9096.png)
您最近一年使用:0次
2023-01-20更新
|
611次组卷
|
5卷引用:宁夏中卫市2023届高三一模数学(文)试题
宁夏中卫市2023届高三一模数学(文)试题江苏省南通市海门区2022-2023学年高三上学期期末数学试题(已下线)模块三 专题12 抛物线 B能力卷(已下线)模块三 专题15 抛物线 B能力卷(已下线)技巧04 结构不良问题解题策略(5大题型)(练习)
名校
2 . 已知函数
.
(1)若
,证明:
;
(2)若
在
上有两个极值点,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d6609f39dfd6a3820204a6e8b5f001.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f751007fe59964fcc05ccb00099a5199.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/261f9fd5f3d2a67143cdf65cca376c73.png)
您最近一年使用:0次
2021-08-16更新
|
250次组卷
|
2卷引用:宁夏中卫市第一中学2022届高三上学期第二次月考数学(文)试题
3 . 已知函数
.
(1)若
,求实数a的值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c9ae84744f3fab61e15886f7e4b2b9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2475f85cc68d0cd775fbacf6eb0c3b2.png)
您最近一年使用:0次
2021-05-10更新
|
515次组卷
|
3卷引用:宁夏中卫市2021届高三第二次优秀生联考数学(理)试题
解题方法
4 . 已知函数
,其中
.
(1)当
,
时,证明:
;
(2)若函数
恒成立,求实数
的取值范围;
(3)若函数
有两个不同的零点
、
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d18b6ae9f8f1c3a527bdd1997ab180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70335f500e874f78cea2949103bb097f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42dd76ab96855910f7e83aee8aa9aee.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/2871a8fc9b28da8f3a885e24f7ce9979.png)
您最近一年使用:0次
5 . 已知点D是圆
上一动点,点
,线段
的中垂线交
于点B.
(1)求动点B的轨迹方程C;
(2)定义:两个离心率相等的圆锥曲线为“相似”曲线.若关于坐标轴对称的曲线T与曲线C相似,且焦点在同一条直线上,曲线T经过点
,
.过曲线C上任一点P向曲线T作切线,切点分别为M,N,这两条切线
,
分别与曲线C交于点G,H(异于点P).
证明:
是一个定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0d586d726f4031e4adbccdd882c18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fd4da08956db1f206c8ea026f4e52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3525ddc5153fada64eaf14e50b536542.png)
(1)求动点B的轨迹方程C;
(2)定义:两个离心率相等的圆锥曲线为“相似”曲线.若关于坐标轴对称的曲线T与曲线C相似,且焦点在同一条直线上,曲线T经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/046f519bdb2972cf7d2f2377c6398b54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2254f7a85430f9c0b1adf193318dbf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491050a33ec5a3177f29931860a6a42b.png)
您最近一年使用:0次
2021-05-10更新
|
907次组卷
|
4卷引用:宁夏中卫市2021届高三第二次优秀生联考数学(理)试题
宁夏中卫市2021届高三第二次优秀生联考数学(理)试题安徽省合肥市2021届高三下学期第三次教学质量检测理科数学试题(已下线)第3讲 圆锥曲线中的证明、定值、定点问题(练)-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)四川省遂宁市大英县大英中学2022-2023学年高三下学期3月月考数学试题
解题方法
6 . 已知函数
.
(1)若
,证明
;
(2)若对任意
,
,都有
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac11472ef53c9f04fdd9030f0cfd3038.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1fa1634d00a91a067feb12dcf03d633.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc4136bd17997e11a7f8abcb19f9018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57fa82ccabf683341da731531e1e8691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0e6d5e4806e6083ed9007576f99915.png)
您最近一年使用:0次
名校
7 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130bd945a5e0f6a4bacb73892d70abca.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc9ec5a0d1f0ddad352975b0e7ef502.png)
您最近一年使用:0次
2020-09-21更新
|
325次组卷
|
4卷引用:宁夏海原县第一中学2021届高三上学期期末考试数学(理)试题
8 . 已知抛物线
:
的焦点为
,倾斜角为45°的直线
过点
与抛物线
交于
,
两点,且
.
(1)求
;
(2)设点
为直线
与抛物线
在第一象限的交点,过点
作
的斜率分别为
,
的两条弦
,
,如果
,证明直线
过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/f1ed9d97b8745ed1c15349ea3fffc299.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bf1c935b01eed783fe5e24fceff383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f56730077a24891460edca8b92e04b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2020-11-29更新
|
1311次组卷
|
4卷引用:宁夏中卫中学2022-2023学年高二下学期第二次综合考试A卷数学(理)试题
名校
解题方法
9 . 已知函数
,其中
,
,e为自然对数的底数.
(1)若
,且当
时,
总成立,求实数a的取值范围;
(2)若
,且
存在两个极值点
,
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85b7ff850be637a766029accc94ed8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/256f3981024e53f373a80aad40e994ae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/3fe07ad8ec94688f0aef0f08a03631d6.png)
您最近一年使用:0次
2020-06-25更新
|
7967次组卷
|
6卷引用:宁夏中卫市2020届高三下学期高考第三次模拟考试数学(理)试题
宁夏中卫市2020届高三下学期高考第三次模拟考试数学(理)试题四川省成都市实验外国语学校2020届高三数学模拟(三)文试题(已下线)极值点偏移专题08极值点偏移的终极套路(已下线)极值点偏移专题06含指数式的极值点偏移问题(已下线)专题6 极值点偏移问题专题11导数研究双变量问题(解答题)
10 . 已知函数
.
求函数
的单调递增区间;
设函数
,函数
.
若
恒成立,求实数
的取值范围;
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0ea6002785d5df3a4870e159de076d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71013e40b47eae7f60ae79297012cfc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f9490631e2c8eb6e57879c27554c62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c512c047783c07da1d4f4455a4033ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392fadea33e5842027b50163955ae554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876959b9f90f2379cf3d0927a8e31005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15142cd3ab6529d6b74123b63610fcce.png)
您最近一年使用:0次