名校
解题方法
1 . 设双曲线的中心为O,右焦点为F,点B满足
,若在双曲线
的右支上存在一点A,使得
,且
,则
的离心率的取值范围是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-01-30更新
|
311次组卷
|
3卷引用:2023新东方高二上期末考数学01
2023新东方高二上期末考数学01浙江省杭州第二中学2023-2024学年高二上学期期末考试数学试题(已下线)2.3.2 双曲线的性质(二十二大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
2 . 已知数列
满足
,且对任意正整数n都有
.
(1)求数列
的通项公式;
(2)设数列
的前n项和为
,
,(
),若
且
,求集合A中所有元素的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f087c4ce33b0755d7fd9c09e23df7e49.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93924bbe26c09cb51112df4c99aed717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e6bdf0a6c7ffc1a35bc9ada47c2d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7117fb89aea6e16857335f7e60bf79.png)
您最近一年使用:0次
2024-01-30更新
|
751次组卷
|
3卷引用:2023新东方高二上期末考数学01
解题方法
3 . 已知函数
,
.
(1)若
,求
在区间
上的最大值;
(2)若关于
的方程
有且只有三个实数根
,
,
,且
.证明:
(ⅰ)
;
(ⅱ)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79588c22361de47a687ccda8449a4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](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/9e11f4ca0e7ace69f92130d0525bcdb3.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4135646a1c78ccade80bac1d30d7a27.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
(ⅰ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fbfe23e06cc72f33f925dd5ee3351e.png)
(ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a77b93203f374e0c1ffccc59776f79.png)
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4 . 已知函数
.
(1)当
时,求
的单调区间;
(2)若函数
的值域为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48beb029095fec0e587f38ff9dde6bf3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02f266bd253738e315e84231235f0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d3ff22333351c909a37c1d1dd19f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
5 . 已知函数
是定义在
上的减函数,其导函数
满足
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05492bbe2597c7ad72568e26df413a4a.png)
A.![]() | B.当且仅当![]() ![]() |
C.![]() | D.当且仅当![]() ![]() |
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名校
解题方法
6 . 已知点A(−2,0),B(2,0),动点M(x,y)满足直线AM与BM的斜率之积为−
.
(1)求M的轨迹;
(2)过坐标原点的直线交M的轨迹于P,Q两点,点P在第一象限,PE⊥x轴,垂足为E,连结QE并延长交M的轨迹于点G.
①证明:
是直角三角形;
②求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求M的轨迹;
(2)过坐标原点的直线交M的轨迹于P,Q两点,点P在第一象限,PE⊥x轴,垂足为E,连结QE并延长交M的轨迹于点G.
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a0a6891259bf27be2280c6b6ba7430.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a0a6891259bf27be2280c6b6ba7430.png)
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7 . 平面直角坐标系中,圆M经过点
,
,
.
(1)求圆M的标准方程;
(2)设
,过点D作直线
,交圆M于PQ两点,PQ不在y轴上.
①过点D作与直线
垂直的直线
,交圆M于EF两点,记四边形
的面积为S,求S的最大值;
②设直线OP,BQ相交于点N,试证明点N在定直线上,求出该直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b42d63fab09f90a520a52c87ab3eb39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab400b66fae56036c1e66c1e0a8fb899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e157d75836912739cfa68013a48f07.png)
(1)求圆M的标准方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d29d7fac4f150927e672507bdb26285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
①过点D作与直线
![](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/ebcad0585886e2d7bac28a0e292a1d37.png)
②设直线OP,BQ相交于点N,试证明点N在定直线上,求出该直线方程.
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8 . 已知圆
过点
,圆心在直线
上,截
轴弦长为
.
(1)求圆
的方程;
(2)若圆
半径小于
,点
在该圆上运动,点
,记
为过
、
两点的弦的中点,求
的轨迹方程;
(3)在(2)的条件下,若直线
与直线
交于点
,证明:
恒为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0778813665f307942db9769077032f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e5eea5f7f98ca8632358b7e49ceb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)在(2)的条件下,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33400b08941f4f9c0ed12b0e0cdff822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975d6f7561fc2bce5f4c94a33b3c0ccf.png)
您最近一年使用:0次
名校
9 . 如图,点C是以AB为直径的圆O上的一个动点,点Q是以AB为直径的圆O的下半个圆(包括A,B两点)上的一个动点,
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a547a90936ff4635dd6d5f303e12986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32979e540e6770ffc0f6417395ec5c74.png)
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解题方法
10 . 如图,已知:
为椭圆
长轴的两个端点,
是椭圆C上不同于A,B的一点,从原点O向圆
作两条切线分别交椭圆C于点M,N,记直线
的斜率分别为
,
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/a15b4490-b2b7-4193-ab89-7b35a738cc61.png?resizew=194)
(1)若圆P与x轴相切于椭圆C的右焦点,求圆P的半径.
(2)若
,求半径r的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbec8b46231e412ddce55cc96634e182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596af38cf818a4e185d02d4d94f94312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c5a4427833e5eb70892521503ea72a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c65902e35640cf2c8d4111c36b40145.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/a15b4490-b2b7-4193-ab89-7b35a738cc61.png?resizew=194)
(1)若圆P与x轴相切于椭圆C的右焦点,求圆P的半径.
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c0d7ea4f1696ad189baf8ea3d294e9.png)
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