名校
解题方法
1 . 已知
.
(1)求
的单调区间和最值;
(2)定理:若函数
在
上可导,在
上连续,则存在
,使得
.该定理称为“拉格朗日中值定理”,请利用该定理解决下面问题:
若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9050ed7a94f79ad5a969b77a80baf52f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)定理:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f0cfa5839f97f252dc0126fa27bfc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8166cc061d434d02bccbcf153cc6b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba089868d2ce3254b25bf625a90689c.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a0a547c81fe36ab8c3ea79622ce7ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c502afc24d9ff9b0f07682a1d0bfa2e.png)
您最近一年使用:0次
2 . 给定正整数
,设数列
是
的一个排列,对
,
表示以
为首项的递增子列的最大长度,
表示以
为首项的递减子列的最大长度.
(1)若
,
,
,
,
,求
和
;
(2)求证:
,
;
(3)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa79f2092161050c26653fd3b0e91c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20681d18e13968fc0d6c7aa9b0c66392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80fdae3edccbdb22b78b114d3c15524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb334e165679c6cb500c994cffa47147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0abedd59476f8793d5a8948590a70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f483a9467cfbb1cd9b636e05247ab9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d46063c5ce508068c8b1f59d39101b.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94536f53897365b8b1d0e89c83738cf6.png)
您最近一年使用:0次
2024-06-10更新
|
375次组卷
|
2卷引用:2024届河北省承德市部分示范高中高三三模数学试题
名校
解题方法
3 . 柯西是一位伟大的法国数学家,许多数学定理和结论都以他的名字命名,柯西不等式就是其中之一,它在数学的众多分支中有精彩应用,柯西不等式的一般形式为:设
,则
当且仅当
或存在一个数
,使得
时,等号成立.
(1)请你写出柯西不等式的二元形式;
(2)设P是棱长为
的正四面体
内的任意一点,点
到四个面的距离分别为
、
、
、
,求
的最小值;
(3)已知无穷正数数列
满足:①存在
,使得
;②对任意正整数
,均有
.求证:对任意
,
,恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a8a1b208f491296432e9e6bf0e91c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0653d6a0e8778ad47b06d5f6b88cffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419c991c4022ef12d4801e119018b587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31a068fb311eff550b3088a212fb2f0.png)
(1)请你写出柯西不等式的二元形式;
(2)设P是棱长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d0252c1b2f7d2a84b5c985d19d547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d31659f106fba3c9750661eb0e3c3eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dde93376f5d29f8f7d501122759b0ab.png)
(3)已知无穷正数数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c24ecf9e59082e563372b12981d03fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee33826e02eda7aa6221649355a5709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9db6b0bf3d360830fff618193c595b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a33ac34aa03dc7f0a5faad6dc664ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
您最近一年使用:0次
2024-05-20更新
|
382次组卷
|
2卷引用:河北省邯郸市2024届高三下学期高考保温数学试题
名校
解题方法
4 . 对于数列
,如果存在等差数列
和等比数列
,使得
,则称数列
是“优分解”的.
(1)证明:如果
是等差数列,则
是“优分解”的.
(2)记
,证明:如果数列
是“优分解”的,则
或数列
是等比数列.
(3)设数列
的前
项和为
,如果
和
都是“优分解”的,并且
,求
的通项公式.
![](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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd84622d5883097a686797889192356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明:如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33119e0b8e033e27fde4505b90a1c3b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238024e8fa2058c5cbbf2f757ce9a997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e274217ecbdfeea729eaa317359e77.png)
(3)设数列
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15ebc127b977d405b867a151696b163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2024-06-11更新
|
939次组卷
|
5卷引用:河北省保定市保定名校协作体2024届高三五月适应性考试(三模)数学试题
5 . 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
名校
6 . 甲、乙、丙三人进行传球游戏,每次投掷一枚质地均匀的正方体骰子决定传球的方式:当球在甲手中时,若骰子点数大于3,则甲将球传给乙,若点数不大于3,则甲将球保留;当球在乙手中时,若骰子点数大于4,则乙将球传给甲,若点数不大于4,则乙将球传给丙;当球在丙手中时,若骰子点数大于3,则丙将球传给甲,若骰子点数不大于3,则丙将球传给乙.初始时,球在甲手中.
(1)设前三次投掷骰子后,球在甲手中的次数为
,求随机变量
的分布列和数学期望;
(2)投掷
次骰子后
,记球在乙手中的概率为
,求数列
的通项公式;
(3)设
,求证:
.
(1)设前三次投掷骰子后,球在甲手中的次数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)投掷
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ba85f74cda4ddd621278e558bc036f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffe6b05ff4e8e312ebdd9f0c17e506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c52b221abebf7af78795fd6eefbf218.png)
您最近一年使用:0次
2024-03-13更新
|
1412次组卷
|
3卷引用:河北省正定中学2024届高三三轮复习模拟试题数学(二)
河北省正定中学2024届高三三轮复习模拟试题数学(二)2024年河南省普通高中毕业班高考适应性测试数学试题(已下线)湖北省武汉市(武汉六中)部分重点中学2024届高三第二次联考数学试题变式题17-22
7 . 对于任意给定的四个实数
,
,
,
,我们定义方阵
,方阵
对应的行列式记为
,且
,方阵
与任意方阵
的乘法运算定义如下:
,其中方阵
,且
.设
,
,
.
(1)证明:
.
(2)若方阵
,
满足
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e84c30444f13d37ada78285dc4f83b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e76d1d8e50dda4d50229a8a20c57e58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc29ee719feeedfbc8c529cf11348abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e11a5b70e1e2e685d1783a4707872e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ec97af19b15cd584710a3faf30c716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f44b167b4e75af29a18637f71f3ebfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b39fcc210ec89dbc7d684a70a34542c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d17ebf9f595cdb9dab841dec703b512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a4ed514630bd37fab9765b3fb5f2cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709d09c76c222f156df31a1bba5f2ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e4a35eca00ea2f4580d62515d54d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95035eeae686e910be45f08093e406c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e7d309cb178b71c6e56f5b7f610413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109b4ece615b08a89a7f69d436f448b0.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addb109c49695bce8c5b5cf4fad95772.png)
(2)若方阵
![](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/2221c60bc15c59fa1b3ac74a23b57cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fa9bfe3bf3e3b7265da3c49d31f1bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35536fb98d8b24cead230c8df95fd9d3.png)
您最近一年使用:0次
2024-06-13更新
|
159次组卷
|
3卷引用:2024届河北省保定市九县一中三模联考数学试题
解题方法
8 . 在某项投资过程中,本金为
,进行了
次投资后,资金为
,每次投资的比例均为x(投入资金与该次投入前资金比值),投资利润率为r(所得利润与当次投入资金的比值,盈利为正,亏损为负)的概率为P,在实际问题中会有多种盈利可能(设有n种可能),记利润率为
的概率为
(其中
),其中
,由大数定律可知,当N足够大时,利润率是
的次数为
.
(1)假设第1次投资后的利润率为
,投资后的资金记为
,求
与
的关系式;
(2)当N足够大时,证明:
(其中
);
(3)将该理论运用到非赢即输的游戏中,记赢了的概率为
,其利润率为
;输了的概率为
,其利润率为
,求
最大时x的值(用含有
的代数式表达,其中
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41d793c851a2f72f787913ba23e459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a22baa009d2d45f6a37332ec3363285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903d7f7559c216e2516b9886c8f96008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e60c0d3a709196db0791a93ed0db409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf99487d7860d017c0747ff966edfd77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad52924df9291d5d191d18e09374ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cdff4a44b674e8060072b7326549bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e60c0d3a709196db0791a93ed0db409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdbd2aa0b04224ad335d43a53d81ae16.png)
(1)假设第1次投资后的利润率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41d793c851a2f72f787913ba23e459c.png)
(2)当N足够大时,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58c4f5f1d988a104655727aa501683c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8f40e552f049c19252845917375c17.png)
(3)将该理论运用到非赢即输的游戏中,记赢了的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5092000864ee720978d6d701c953a388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c5439464042af3cbd35cf65be156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a89183e464e81e2c692ed239023ecd.png)
您最近一年使用:0次
9 . 已知抛物线
的焦点为
,过
且倾斜角为
的直线
与
交于
,
两点.直线
,
与
相切,切点分别为
,
,
,
与
轴的交点分别为
,
两点,且
.
(1)求
的方程;
(2)若点
为
上一动点(与
,
及坐标原点均不重合),直线
与
相切,切点为
,
与
,
的交点分别为
,
.记
,
的面积分别为
,
.
①请问:以
,
为直径的圆是否过定点?若过定点,求出该定点坐标;若不过定点,请说明理由;
②证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889c77ab62cad9151cfe679b8181d445.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029ad83f1a3262048cba0e650b63e929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a019625b21ba728a67a3f6437709ace4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
①请问:以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
10 . 已知动点
与定点
的距离和
到定直线
的距离的比为常数
.其中
,且
,记点
的轨迹为曲线
.
(1)求
的方程,并说明轨迹的形状;
(2)设点
,若曲线
上两动点
均在
轴上方,
,且
与
相交于点
.
①当
时,求证:
的值及
的周长均为定值;
②当
时,记
的面积为
,其内切圆半径为
,试探究是否存在常数
,使得
恒成立?若存在,求
(用
表示);若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7a6fd6d651ae341154c2e40928d628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4988bd24f9af3f2b3c59aae61ca47ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be44077d42cfffece905b1af13e000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d812643e080d4d447fab7fe2ae2646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240ed21d7e90d10088ad597fca655100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf2957b0a640070e941253e6d6d8be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba58e749d3c9f94abf0cc4743b8bc4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207a808ffbeb016857125fbd530e0d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00fdefb61da9119bdf6093ac2b9e7de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
您最近一年使用:0次
2024-02-29更新
|
5208次组卷
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7卷引用:2024届河北省承德市部分高中二模数学试题
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