1 . 已知圆
,定点
,D是圆A上的一动点,线段DB的垂直平分线交半径DA于点E.
(1)求点E的轨迹方程;
(2)若直线m与点E的轨迹交于M,N两点,与圆
相交于P,Q两点,且
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db913f194627b21fae0c9ceaf40033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513eafd10fa1ec0196562865517e0b09.png)
(1)求点E的轨迹方程;
(2)若直线m与点E的轨迹交于M,N两点,与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcc2501b8ea3dd150e3d8f02f0bd174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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解题方法
2 . 在棱长为2的正方体
中,
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/24/555c771c-8b93-4469-a840-0d43cd9d9ac4.png?resizew=152)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68345111b4081c514cc15ee82167898f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02b7a2a4601a4a52dc2638845eae3b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/24/555c771c-8b93-4469-a840-0d43cd9d9ac4.png?resizew=152)
A.![]() |
B.三棱锥![]() |
C.若![]() ![]() ![]() |
D.三棱锥![]() ![]() |
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3 . 已知函数
.
(1)求
的图象的对称中心、对称轴、单调递增区间;
(2)当
时,求
的最值.
(3)当
时,关于
的不等式
有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3839dbbf132fc23661b92397964bfb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/691c1fc50ea793ea08748cb75bae70e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e74fc7479e44217bfa27dbd75992b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf755154fdddb396e7ed1a2352f1911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知函数
,下列四个命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde2a965644fb3271f5d1499a6d0f1a8.png)
A.函数![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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5 . 已知函数
在区间
上单调,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32906d5d903b746760df451a828780c7.png)
______ ;函数
在区间
上恰有5个零点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732a339581df8f5cec4b8abddb777e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37fb9ead0e9436b60bb8f82eaa64782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32906d5d903b746760df451a828780c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b929d10624c0bb2db150588694b9dba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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6 . 在平面直角坐标系
中,已知F为抛物线
的焦点,点
在该抛物线上且位于x轴的两侧,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306b21a5d7e68f1992e5797b4368ed56.png)
A.![]() |
B.直线AB过点![]() |
C.抛物线在A处的切线和在B处的切线相交于点M,则点M在直线![]() |
D.![]() ![]() |
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解题方法
7 . 已知
为
上的奇函数,
为
上的偶函数,且
.
(1)求函数
的解析式;
(2)若关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06678bd554270860e09df57d23fd43b8.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9752a12c31adb8bc7363b78adb32ce58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若不等式
,
恒成立,求实数a的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e442b944a03e22fe96d18d4a7f33a9dd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f832d9cca2d5c9d76d38374e2a258d9.png)
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解题方法
9 . 设双曲线
的左、右焦点分别为
,过坐标原点的直线与
交于
点,
,则
的离心率为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db0cc24753f6ea44c19c3cc49e26024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/654ac5370193ceb23b2de359d52a3344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2024-02-29更新
|
484次组卷
|
5卷引用:河北省石家庄精英中学2023-2024学年高二上学期期末数学试题
河北省石家庄精英中学2023-2024学年高二上学期期末数学试题吉林省四校2023-2024学年高二下学期期初联考数学试题重庆市铜梁中学校2023-2024学年高二下学期开学考试数学试题(已下线)专题15 双曲线离心率(一题多解)(已下线)第1题 双曲线的离心率问题(5月)(压轴小题)
名校
解题方法
10 . 已知双曲线
的离心率为
,点
分别是双曲线的左右焦点,过
的直线交双曲线右支于P,A两点,点P在第一象限,当直线PA的斜率不存在时,
.
(2)线段
交圆
于点B,记
的面积分别为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f103bf5165f87bbd99090ee8cc50fe.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa46bcef998ac174ca0f564fc39b667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed4138590ae2a43a383663f3cff223e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc4ea29a512c7979a09adcff888ed7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51da7a6689fcd857bdafe8b9aef58231.png)
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