1 . 已知定点
,
轴于点H,F是直线OA上任意一点,
轴于点D,
于点E,OE与FD相交于点G.
(1)求点G的轨迹方程C;
(2)过
的直线交C于P,Q两点,直线AP,AQ的斜率分别为
和
,证明:
为定值;
(3)在直线
上任取一点
,过点B分别作曲线C:
的两条切线,切点分别为M和N,设
的面积为S,求S的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179fe7eff7abfdd092b63c9c1b82d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7277dcfb480720f2f37413cb0d34d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e7ec9f3e17dbb0362a8c9aac629a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a91621dc26d771853fd1f0d9bdf04c7.png)
(1)求点G的轨迹方程C;
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef66a0582e95fb5c57a405acdea9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1efe96e7776f1b5dfa92c295f8d97d.png)
(3)在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/906fc0c4a747cfa348986baefbd02752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d0469336f71edd52dc9148c67db052.png)
您最近一年使用:0次
2 . 已知数列
和
满足:
.
(1)设
求
的值;
(2)设
求数列
的通项公式;
(3)设
证明:______.
请从下面①,②两个选项中,任选一个补充到上面问题中,并给出证明.
①
;②
其中
.
注:若两个问题均作答,则按第一个计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08416257a7c5427d9266e9ee46ee492b.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb3a4652ccd6c113de9645852973d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08360bbdf8e90d7d35445ea6e9923658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a27e634b912cd518c69ff3ffb74db8.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc35823313a638d6dcf399efaeff9e0.png)
请从下面①,②两个选项中,任选一个补充到上面问题中,并给出证明.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51206c051804c48be676c6510c63ce3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b09b55a8bc170344adf78ee08ea8892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce671943072553870e3c059e835e980c.png)
注:若两个问题均作答,则按第一个计分.
您最近一年使用:0次
名校
解题方法
3 . 某汽车厂商生产某型号具有自动驾驶功能的汽车,该型号汽车配备两个相互独立的自动驾驶系统(记为系统
和系统
),该型号汽车启动自动驾驶功能后,先启动这两个自动驾驶系统中的一个,若一个出现故障则自动切换到另一个系统.为了确定先启动哪一个系统,进行如下试验:每一轮对系统
和
分别进行测试试验,一轮的测试结果得出后,再安排下一轮试验.当一个系统出现故障的次数比另一个系统少2次时,就停止试验,并认为出现故障少的系统比另一个系统更稳定.为了方便描述问题,约定:对于每轮试验,若系统
不出现故障且系统
出现故障,则系统
得1分,系统
得-1分;若系统
出现故障且系统
不出现故障,则系统
得-1分,系统
得1分;若两个系统都不出现故障或都出现故障,则两个系统均得0分.系统
出现故障的概率分别记为
和
,一轮试验中系统
的得分为
分.
(1)求
的分布列;
(2)若系统
和
在试验开始时都赋予2分,
表示“系统
的累计得分为
时,最终认为系统
比系统
更稳定”的概率,则
,
,其中
.现根据
的值来决定该型号汽车启动自动驾驶功能后先启动哪个系统,若
,则先启动系统
;若
,则先启动系统
;若
,则随机启动两个系统中的一个,且先启动系统
的概率为
.
①证明:
;
②若
,由①可求得
,求该型号汽车启动自动驾驶功能后无需自动切换到另一个自动驾驶系统的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)若系统
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82078c39ec148befeb0011cc261a51c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e86f01de277cfcf6c293f35f5fdf2bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59c570f0c7b0702dfdb16088da7ec86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246e3c7846e0d306ed9006b77e7b7697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25444b9b87ffa695464502f5e8864fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e5dc72fd2623e4766994baf3fbabc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ef764dca7fcf36caa9395387ddf4f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75d40514ea42bc2a92a25840a0b2251.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97df32a5e8c500aca06215fe46836999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91691dece5b2d47cf1fcc0797c817548.png)
您最近一年使用:0次
2024-05-23更新
|
601次组卷
|
3卷引用:福建省漳州市2024届高三毕业班第四次教学质量检测数学试题
名校
4 . 已知定义在
上的函数
,若存在实数
,
,
使得
对任意的实数
恒成立,则称函数
为“
函数”;
(1)已知
,判断它是否为“
函数”;
(2)若函数
是“
函数”,当
,
,求
在
上的解.
(3)证明函数
为“
函数”并求所有符合条件的
、
、
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d637d748a2b196af6d91703881ae1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67758380edd3796902534cf0e52cb6a1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9697e701323f29c2b8fb4b69fdec2a50.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901a683d7456f2b2135bccb41e70e33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad324be3bebd9c8051c5f502df2b536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51870c1132971c292e4498255210546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4947f55ebd9b5438e46cb120d51be615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966055559e213bce8e92ef59ba03d2d4.png)
(3)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa79143526cf263a8fff8030446efa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67758380edd3796902534cf0e52cb6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
5 . 在平面直角坐标系中,
是双曲线
位于第二象限左支上一动点,过点
作直线交
轴正半轴于点
,交双曲线右支于
,再过点
作直线交双曲线右支于
,总有
,记直线
的斜率为
,直线
的斜率为
,直线
的斜率为
,且
.当
三点共线时.求证:
(1)
为常数;
(2)
为定点,并求其坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5441e93d0fdb6558b4ba2010d6b92897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c220eadc312101e2fb89dfe920f7b30d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d200a411fbc2f50ad72f1fd729a7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1e01fd4a5d215c46194cd1fc4a3dd1.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279921f968ec1782d04dda1a1facbc50.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
解题方法
6 . 对于定义域在
上的函数
,定义
.设区间
,对于区间
上的任意给定的两个自变量的值
、
,当
时,总有
,则称
是
的“
函数”.
(1)判断函数
是否存在“
函数”,请说明理由;
(2)若非常值函数
是奇函数,求证:
存在“
函数”的充要条件是存在常数
,使得
;
(3)若函数
与函数
的定义域都为
,且均存在“
函数”,求实数
的值.
![](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/8d25597c0f369019a0901849bc12da1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb71b8c83c4f5a3146e3871b6308d4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61c8d37c767ba727cc7f5f7e00a7d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6f99885e464b84f1dc2b897070cbdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若非常值函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d314b6f3729e70a0d0c60414aec69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c9418985f008bb9ab6482930f187dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950c0c0b3b3c63fd0e7700e22c0f7bd9.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d17dcc171997459b17118083b339145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccbf6c35d8fc9e12a15cc7e0643ca35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-01-13更新
|
518次组卷
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6卷引用:上海市东华大学附属奉贤致远中学2023-2024学年高一上学期12月教学评估数学试题
上海市东华大学附属奉贤致远中学2023-2024学年高一上学期12月教学评估数学试题上海市奉贤区2022-2023学年高一上学期1月期末练习数学试题(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列(已下线)单元高难问题03函数恒成立问题和存在性问题-【倍速学习法】(沪教版2020必修第一册)(已下线)专题14函数的基本性质-【倍速学习法】(沪教版2020必修第一册)江西省上饶市婺源天佑中学2023-2024学年高一上学期期末模拟数学试题
解题方法
7 . 现有甲、乙两个不透明盒子,都装有1个红球和1个白球,这些球的大小、形状、质地完全相同.
(1)若从甲、乙两个盒子中各任取一个球交换放入另一个盒子中,
次这样的操作后,记甲盒子中红球的个数为
.求
的分布列与数学期望;
(2)现从甲中有放回的抽取
次,每次抽取1球,若抽取次数不超过
次的情况下,抽取到2次红球,则停止抽取,一直抽取不到2次红球,第
次抽取完也停止抽取,令抽取停止时,抽取的次数为
,求
的数学期望
,并证明:
.
(1)若从甲、乙两个盒子中各任取一个球交换放入另一个盒子中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6368fec0c2c25db7c29b014d60270e97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
(2)现从甲中有放回的抽取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bedb7b3610d86273097614a9b3b6078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71701db4b413f2364dbcbd612fbc8a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eda9982a3b268dc3904eb16e1b89f9d.png)
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解题方法
8 . 设Sn是数列
的前n项和,定义等斜率数列
且
等式
恒成立.
(1)若
是首项为1,公比为3的等比数列,请判断
是否为等斜率数列,并说明理由;
(2)已知
是等斜率数列,证明:
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0e0373a4e95709a67c312cdc054466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d48bb696708fd77448c1427b6e769fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d0c1a0bddea64281c61f2851b37634.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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9 . 设椭圆C:
的左、右顶点和椭圆
的左、右焦点均为E,F.P是C上的一个动点(异于E,F),已知直线EP交直线
于点A,直线FP交直线
于点B.直线AB与椭圆
交于点M,N,O为坐标原点.
(1)若b为定值,证明:
为定值;
(2)若直线OM,ON的斜率之积恒为
,求b.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8c4b0e11e5894346b27e4656336c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e7a9b887d3dca1953a4f271d7b60a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f09e84f509537abd3dfaa20d7915675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee023dde0cd66b17a3ec5775d4b7d714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)若b为定值,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b0ba14e41e306e5633ad4bf1cdedd8.png)
(2)若直线OM,ON的斜率之积恒为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
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名校
解题方法
10 . 在初等数论中,对于大于1的自然数,除了1和它自身外,不能被其它自然数整除的数叫做素数,对非零整数a和整数b,若存在整数k使得
,则称a整除b.已知p,q为不同的两个素数,数列
是公差为p的等差整数数列,
为q除
所得的余数,
为数列
的前n项和.
(1)若
,
,
,求
;
(2)若某素数整除两个整数的乘积,则该素数至少能整除其中一个整数,证明:数列
的前q项中任意两项均不相同;
(3)证明:
为完全平方数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8b048de4625c67d7f74a4eda94877a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451b1923f70f26e57c557ffe606f7016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addee6ce5163a2580888ce2da22714af.png)
(2)若某素数整除两个整数的乘积,则该素数至少能整除其中一个整数,证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ab4a56d5549a49adae4f1f17926dd8b.png)
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