1 . 已知函数
.
(1)讨论
的单调性;
(2)若方程
有两个不相等的实根
,
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef92a1b21dee16b769b344f033d6d23.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ab0c9b89b443de5dae60b69a94d9a0.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/2b4b6596ddd986c70c89171c047693ba.png)
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名校
解题方法
2 . 椭圆
与双曲线
有相同的焦点,且过
.
(1)求椭圆
的方程;
(2)如图所示,记椭圆的左、右顶点分别为
,
,当动点
在定直线
上运动时,直线
,
分别交椭圆于两点
,
.
(i)证明:点B在以
为直径的圆内;
(ii)求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffb877445206ef92ce21c0856c5408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/2eea8918-94ca-4ef3-bd39-183eade5b525.png?resizew=173)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图所示,记椭圆的左、右顶点分别为
![](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/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(i)证明:点B在以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(ii)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
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2023-11-29更新
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4卷引用:山东省青岛市青岛第二中学2023-2024学年高二上学期期中数学试题
名校
3 . 已知函数
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a7d37824a7e361d0cfcfdb372c87e7.png)
A.函数![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.不等式![]() ![]() ![]() ![]() |
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5卷引用:山东省名校考试联盟2023-2024学年高三上学期期中检测数学试题
名校
4 . 已知函数
.
(1)求函数
的单调区间;
(2)若方程
的两根互为相反数.
①求实数
的值;
②若
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5666e2041f0ca951e9cdd53fd7c88a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/022a375072c113ab3efaa8756251e403.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee4e4ef6bc78dc8e69bf99c2807b7b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ba4e9c6b559968f2f637043af15817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8c484b0027dcd3111ea15aa9717c73.png)
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2023-11-26更新
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3卷引用:山东省日照市2024届高三上学期期中校际联合考试数学试卷
23-24高二上·山东德州·期中
名校
解题方法
5 . 抛物线C:
,过焦点F的直线l与抛物线C交于A,B两点(点A在第一象限),
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cf8af6e62058cc4e2d83d5da7f4c68.png)
A.![]() |
B.![]() |
C.当直线l的倾斜角为60°时,![]() ![]() |
D.当直线AM与抛物线C只有一个公共点时,![]() |
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2023-11-23更新
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4卷引用:山东省德州市2023-2024学年高二上学期期中考试数学试题
(已下线)山东省德州市2023-2024学年高二上学期期中考试数学试题河南省信阳市信高教育集团南湾校区2023-2024学年高二上学期期末复习检测数学试题(一)河南省信阳市固始县高级中学第一中学2023-2024学年高二上学期第三次月考数学试题(已下线)期末精确押题之多选题(40题)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)
名校
解题方法
6 . 已知函数
,
,则下列说法正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bd8a100f995d01627c3cb6a2ae8c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b9d6be01fc9d47f5965f32d767b742.png)
A.函数![]() ![]() |
B.当![]() ![]() ![]() |
C.若函数![]() ![]() ![]() |
D.若不等式![]() ![]() ![]() |
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3卷引用:山东省济宁市2024届高三上学期期中考试数学试题
名校
解题方法
7 . 已知函数
.
(1)若
,判断函数
的单调性,并说明理由;
(2)若
时,
恒成立.
(i)求实数
的取值范围;
(ⅱ)证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231f6f4415a7cef9ad2c46b6f0668050.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(i)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18691198792f7da0f054fd2db6d376c1.png)
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3卷引用:山东省日照市五莲县第一中学2024届高三上学期期中考试数学模拟试题
8 . 已知椭圆C:
的离心率为
,点
在椭圆上.直线
与椭圆交于
两点.且
,其中
为坐标原点.
(1)求椭圆
的方程;
(2)若过原点的直线
与椭圆
交于
两点,且过
的中点
.求四边形
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca18783e2f3bf03b3fadd62473af700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc11e7549cfce9220e70250ac943e457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过原点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
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4卷引用:山东省滨州市惠民县2023-2024学年高二上学期期中数学试题
山东省滨州市惠民县2023-2024学年高二上学期期中数学试题江苏省连云港市华杰高级中学2023-2024学年高二上学期期中数学试题河北省2024届高三上学期学生全过程纵向评价(一)数学试题(已下线)重难点突破17 圆锥曲线中参数范围与最值问题(八大题型)
名校
解题方法
9 . 已知点
在双曲线
上.
(1)双曲线上动点Q处的切线交
的两条渐近线于
两点,其中O为坐标原点,求证:
的面积
是定值;
(2)已知点
,过点
作动直线
与双曲线右支交于不同的两点
、
,在线段
上取异于点
、
的点
,满足
,证明:点
恒在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be3ad3dd6803d92df6ff8a80cd35095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2702066c515f9b77353cfba5f9e33c0.png)
(1)双曲线上动点Q处的切线交
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb41efe7bf6a0c35c940d68d85bd928a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad01b0639b0b618c9128df2a5d1315c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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2023-05-17更新
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4卷引用:山东省青岛市青岛第二中学2023-2024学年高二上学期期中数学试题
山东省青岛市青岛第二中学2023-2024学年高二上学期期中数学试题安徽省舒城中学2023届仿真模拟卷(二)数学试题(已下线)专题3.9 圆锥曲线中的定点、定值、定直线问题大题专项训练【九大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)专题突破卷23 圆锥曲线大题归类
名校
解题方法
10 . 已知双曲线
的右焦点为
,
的两条渐近线分别与直线
交于
,
两点,且
的长度恰好等于点
到渐近线距离的
倍.
(1)求双曲线的离心率;
(2)已知过点
且斜率为1的直线
与双曲线交于
,
两点,
为坐标原点,若对于双曲线上任意一点
,均存在实数
,
,使得
,试确定
,
的等量关系式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.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/0fa5d6092f598c7da4796f965e40525a.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求双曲线的离心率;
(2)已知过点
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9909ded4aa86b799e374c53a11a3c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
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5卷引用:山东省菏泽市2023-2024学年高二上学期11月期中考试数学试题(B)