名校
1 . 已知实数x,y满足方程
.
(1)求
的值;
(2)设
与
是方程组
两组不同的解,其中
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1beb6812158ca2a3082bd13ca07578f0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1afbc87ccffbc98b9ab58df8c69bee.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99307ab4373fbe72422ae5aa980db61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41039d45e37899d233232de3d802b105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccee8eb181dc117834582bc433eca559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab3cf6695638d5bcd26580174d7cbf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da3ff6f17be99ec311610efa08ba002.png)
您最近一年使用:0次
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2 . 对于定义在
上的函数
,如果存在一组常数
,
,…,
(
为正整数,且
),使得
,
,则称函数
为“
阶零和函数”.
(1)若函数
,
,请直接写出
,
是否为“2阶零和函数”;
(2)判断“
为2阶零和函数”是“
为周期函数”的什么条件(用“充分不必要条件”“必要不充分条件”“充要条件”或“既不充分也不必要”回答),并证明你的结论;
(3)判断下列函数是否为“3阶零和函数”,并说明理由.
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f4cc0837a4e6dcd0072887e4e2704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe6d9f54a34762aadfdf8e2bac977cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892519541cfba6f2763cd29159bf1b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329fb959f16f82835aa68fca9d3f08f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcda6a21da79726f8fb3ba6235b9010f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebef85c05f6d84ceb67d92abf77ba2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ace630100e64ed290d82936ad249c8.png)
(2)判断“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)判断下列函数是否为“3阶零和函数”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab7da79b2400cf8125ef040cd056b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321b15db96dc89f136a7421e09fc9814.png)
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2024·全国·模拟预测
名校
解题方法
3 . 已知直线
和椭圆
.
(1)证明:
与
恒有两个交点;
(2)若
为
与
的两个交点,过原点且垂直于
的直线交
于
两点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b648c913b1b66abb9cd526dd8a7b2ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0b0ae6048bf94ccd5a3b4a8aafd81e.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce9db8bf6dff7b5b1feb849f5532f22.png)
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4 . 设函数
为定义在区间
上的可导函数,记
的导函数为
,若对
,都有
或
恒成立,则称
为区间
上的“原导同号函数”.
(1)证明:
为
上的“原导同号函数”;
(2)是否存在实数
,使
为
上的“原导同号函数”,若存在,求出
的取值范围;若不存在,请说明理由;
(3)若
为
上的“原导同号函数”,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126f7f1e8cdd38225803c6ec59968660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a935456da83aed9c3f485152e541f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36489856ced75bf35dea7b12c2b6bcd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14ce24da9de20311832866834d78a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6146c34c9aad4d49938e086d3b18c774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8845c0d06613fabb0358d5392cca38b3.png)
您最近一年使用:0次
名校
解题方法
5 . 曲率是曲线的重要性质,表征了曲线的“弯曲程度”,曲线曲率解释为曲线某点切线方向对弧长的转动率,设曲线
具有连续转动的切线,在点
处的曲率
,其中
为
的导函数,
为
的导函数,已知
.
(1)
时,求
在极值点处的曲率;
(2)
时,
是否存在极值点,如存在,求出其极值点处的曲率;
(3)
,
,当
,
曲率均为0时,自变量最小值分别为
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd817a1014876a72ad1971548ed6f52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe7522a3f232bd0b7a7850ae674db43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad7aa241de8ac2738629f7361a7c8bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea058d082b5f7517c3b6a6359dbcb44a.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c51e20ceeca65fe6821130d94b794c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3387f1c69de6c2407212536b35150e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.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/6fb22f6880c74b35a8285cbb51a50fb1.png)
您最近一年使用:0次
2024-05-23更新
|
265次组卷
|
3卷引用:黑龙江省哈尔滨市第三中学校2023-2024学年高二下学期期中考试数学试卷
黑龙江省哈尔滨市第三中学校2023-2024学年高二下学期期中考试数学试卷湖北省荆州市沙市中学2023-2024学年高二下学期6月月考数学试题(已下线)拔高点突破05 函数与导数背景下的新定义压轴解答题(九大题型)
名校
解题方法
6 . 柯西中值定理是数学的基本定理之一,在高等数学中有着广泛的应用.定理内容为:设函数
,
满足①图象在
上是一条连续不断的曲线;②在
内可导;③对
,
.则
,使得
.特别的,取
,则有:
,使得
,此情形称之为拉格朗日中值定理.
(1)设函数
满足
,其导函数
在
上单调递增,判断函数
在
的单调性并证明;
(2)若
且
,不等式
恒成立,求实数
的取值范围;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9b92a1988f20c45e8ba3887eeb6b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce5b83b652a50ea15c83c826d8fb52f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38593523a246f9e59688f64444e0dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a1212aca40e8dfbb97ae428c5d40a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4306fb6d5419322b4b7b9140e06e43a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38593523a246f9e59688f64444e0dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584ef8a5b63c5a2a80372865ac0cc0a0.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acaa791feb147bd1a8bf5eb4f81a0cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a4b4a9b7f0a8c3de045fe903204800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e71b49ac6c97943138bed91aab6215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d64f25e0020c3db48bb6a767afa98a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19cf16fd398ad9782cd4f5149d0c76f.png)
您最近一年使用:0次
名校
解题方法
7 . 在平面直角坐标系
中,直线
交椭圆
于
两点,点
关于
轴的对称点为
.
(1)用含
的式子表示
的中点坐标;
(2)证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e3cc60d53da732d35fb070e71a97826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0b4bbfa0ed04cd3c2454d99d64e29c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(1)用含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea68142955809f9f40b15e3fa0f5bdd5.png)
您最近一年使用:0次
解题方法
8 . 利用曲线的切线进行放缩:设
上任意一点
的横坐标为
,则过该点的切线方程为
,即
,由此可得与
有关的不等式
,其中
,等号当且仅当
时成立;设
上任意一点
的横坐标为
,则过该点的切线方程为
,即
,由此可得与
有关的不等式:
,其中
,等号当且仅当
时成立,设
是
在点
处的切线
(1)求
的解析式
(2)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
(3)设
,若
对
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fbb4aa41ac2ae85f8f01175d56973c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe9fd326374f2b6e740b6af358e5477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad040ae0fab73f5dd7b1af48cd3b5f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888e7018ffc0049cd7c8eef74af0365d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc59b8f30866d2518b2fcf51072c61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e266dbe1c3244001a75a8cd9cb0576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7afb62af76c4655a9e7203617079c8d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c7d5aee3615cdb65b3dd4e24da7bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee3ff7fe9f4a53f93ef0b825b6bf0c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bca6c04ec232aa3ecc1268289271654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1be7302f2e9ff02fee3fcf26e77b1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/428d922e63d8a0838da6fdacee919ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bafed5b670d33e0fb3bc7bd4dd46f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0769db255cf03e3e213d629970ca70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
9 . 已知
与
都是定义在
上的函数,函数
图像上任意两点
,记
表示此两点连线的斜率.当
时,都有
,则称
是
的一个“T函数”.
(1)判断
是否为函数
的一个
函数,并说明理由;
(2)设
的导数为
,求证:关于
的方程
在区间
上有实数解;
(3)函数
的导函数存在记为
,即
导函数存在记为
,当
都有
,函数
是否存在T函数?若存在,请求出
的所有
函数;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1dc007e36c78ab98df4cd2383b4c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3861f863fc3d8703abf9e5bf97ef6117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a43b43650ed3473888a95607908644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ff3dc91272a2244b4d76056967e9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591c5b712dc14517e369be2345526fc7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c513ef355a637fff90a3371dc5328a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa852120429d7db38eb6266cf9d0d152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d98da166934830f1cfdbcd48dbfea6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2287352f6b9c1ef9e35d2ac6670fcbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e82f423c1c5d304766d1a22d72f042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34367bca1e9f02459dc301e4881edbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591c5b712dc14517e369be2345526fc7.png)
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10 . 已知双曲线
的右顶点为
是双曲线
上两点,过
作斜率为
的直线
,
与双曲线只有
点这一个交点.
(1)求双曲线
的方程;
(2)若
是以
为直角顶点的等腰直角三角形,求
的面积;
(3)已知点
和双曲线上两动点
,满足
,过点
作
于
点,证明:
点在一个定圆上,并求定圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e7542516ded0ce4b169a851da1f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a4ba61e0fe0cb463581292835301f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47f2874795e9df280e3e0bec171358e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a447cd7d35c87c29590a75468adcaf3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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