名校
解题方法
1 . 已知椭圆
的中心在原点,焦点在
轴上,且离心率为
,一个顶点为
.
(1)求椭圆
的标准方程;
(2)设直线
与椭圆交于
两点,
是椭圆上位于直线
两侧的两个动点.若直线
的斜率为
,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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc43e72034cfce8e9d75b55c537287c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
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名校
解题方法
2 . 若一个圆的圆心是抛物线
的焦点,且该圆与直线
相切,则该圆的标准方程为__________ . 过点
作该圆的两条切线
,切点分别为
,则直线
的方程为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088fcdd595455906a1a7080d630611f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d0b13a6875a9fde18f435ba9fe9975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d8cc13666ef5e288a3c98e2fc56aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-01-13更新
|
294次组卷
|
2卷引用:江苏省镇江市镇江一中2022-2023学年高二上学期12月月考数学试题
名校
3 . 已知直线
和以
为端点的线段无公共点,则实数
的取值范围为_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87fa8cdb0b90bcd4620c8d263b2e9677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79f80e2f68fd5cc77510243dea922fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
4 . 已知正项等比数列
的前
项和为
,且
,则公比
的值为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a3885dba73b6cc430fb238b5b349efd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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5 . 已知数列
满足:
.
(1)求
,由此猜想并直接写出数列
的通项公式;
(2)记
,求
;
(3)在(2)的条件下,记
,证明: 当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c54152bbb480300b1cbaca0b0325bd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec99c57bf7997bd93e1ed8f48d5af9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bcd4a2a9d6ece0e6ceedf2b8b60ed81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)在(2)的条件下,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd2d540aa82078d246c1beedd8a8000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ecffd0ede40b23fa293b4f07043329.png)
您最近一年使用:0次
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6 . 已知
,则 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b25d7d11c49974e9e6a4a1a90533b9.png)
A.存在 2 个不同的![]() ![]() ![]() |
B.存在 2 个不同的![]() ![]() ![]() ![]() |
C.存在 2 个不同的![]() ![]() |
D.存在唯一的![]() ![]() ![]() |
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名校
解题方法
7 . 已知奇函数
,其导函数
,则以下命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187a355cbbb4cfbacac738b560acae79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2016e18a010eb6ae81f7b856eb583e.png)
A.![]() |
B.函数![]() |
C.函数![]() |
D.函数![]() |
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8 . 设正整数
,其中
. 记
, 则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f281f36ec4b671651fea5ad7dec6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224fcd92fb32848731a27b3b73a3b602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbff6f8fe8315e4bffc8e54bc0a17921.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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9 . 已知定点
和一动点
,若
,则动点
的轨迹方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125386122811a133ad6e70446900cbc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f595683f69d5d6b5ca76408b0ff6ff17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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10 . 已知
,则 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389f233195d7a44b87503bbc08ecdd6e.png)
________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbcd5da4af1cffdd02b648a8f90203d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389f233195d7a44b87503bbc08ecdd6e.png)
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