1 . 已知椭圆
,点
在椭圆上,如图,用
表示椭圆在点
处切线的单位向量.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/198f7b15-d256-45b8-8ad4-3cc9057793bf.png?resizew=120)
(1)设
,求
的最大值;
(2)是否存在定圆
,使得圆
的任一切线与
的交点
满足
,若存在,求出圆
方程,若不存在,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a6e483672a226118dff5a39aa28449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4fbb5a4568dd3e4baec9f8358552b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e8744362c6e224146461b97faf9821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/198f7b15-d256-45b8-8ad4-3cc9057793bf.png?resizew=120)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75874285daf265905257368573ded035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)是否存在定圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a21698cc2ceabd28d995692ab2bfc7.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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解题方法
2 . 已知向量
满足
,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65aa82ef3ccd07b92895835040b25d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cfe95f520c7b454ceabb2ae9af0a87.png)
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3 . 已知关于x的不等式
对任意
恒成立,则实数a的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b30ba897503f5e37d7005774c0c225d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103ec0d91228a7a0c07a0e2f7bf2b0b6.png)
您最近一年使用:0次
4 . 已知
,其中a,
,则n的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be80de677aadad3c15f8ab9d77acf0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c498307848129bbd89b5b86f511f0f.png)
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5 . 已知锐角
的内角A,B,C的对边分别为a,b,c,且
,则角A的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff214d99784c6b23b7784bdaf3ed37a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad10dcd98c90c20c5acbfe7d83f54d89.png)
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6 . 已知
,
,
,
,1,2,…,则满足
的最小正整数n为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d22ac81dfffec9c7eabf4119eea7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9675214dcec606b8b95fc40f3c1e07e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47b4c70672d5cdb3079f7d6ef0b8395b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbde97699a18dfed26535425ad37fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ea26b90e2f223146b6e88a12e99df8.png)
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7 . 二项式
的展开式中,整数项共有______ 项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7846abcd024558c6369f597261140c22.png)
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8 . 已知点
,抛物线
,不过点P的直线l交抛物线C于不同的两点A,B.记直线
,
的斜率分别为
,
,且满足
,则直线l的斜率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7e1fef7c52d918f9c1c26306fc3e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c2d5ba20426f126eaba9d9cc895e7.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/2562424a83aae7e4b3f8adf90307961a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b58edb637c5dfa03794f3952de9d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ca7188816bab0bbf1543680108b71d.png)
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9 . 设锐角
,O,H分别为其外心和垂心,直线
分别交
,
于L,K.已知
与
的面积相等,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8db9f09c5f5d6cdbf2c48d1ab600488.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff214d99784c6b23b7784bdaf3ed37a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4cd68cc82e90a5e2049a7ea3171b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54435ea54b0214eb58ce6f4a4c53317d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1eb72c3df18cdaa2ff9510b4742dfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8db9f09c5f5d6cdbf2c48d1ab600488.png)
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10 . 函数
的定义域为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a9adff8460c897d079ccf7354dbcd7.png)
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