解题方法
1 . 已知椭圆
过点
,且焦距为
.
(1)求椭圆
的标准方程;
(2)过点
作两条互相垂直的弦
,设弦
的中点分别为
.证明:直线
必过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc3e47a358860345e74450ce2af9f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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解题方法
2 . 已知不等式
对任意的实数x恒成立,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c0050be29ca573dd25c21ecb8a7718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
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2024-03-27更新
|
1248次组卷
|
3卷引用:2024届内蒙古自治区包头市高三下学期二模数学(理)试题
3 . 已知函数
,若
,现有下列4个结论:①
;②
;③
;④
.则其中正确的有__________ .(填上你认为所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc37c1b3f322168d019434bece238cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ab99a5ccd1c64ee0a06942b5ec361e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5f0d374837655cc286d326305da36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed37ee7432002cd0e0978b2012e184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b69c6cc00e7b9725e88070c1ff7022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d0103789c3733b688552031fbe5d49.png)
您最近一年使用:0次
4 . 已知椭圆
:
,
是
的一个焦点,
是
上一点,
为
的左顶点,直线
与
交于不同的两点
,
.
(1)求
的方程;
(2)直线
,
分别交
轴于
,
两点,
为坐标原点;在
轴上是否存在点
,使得
,若存在,求出点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c9bebea391a1f9956dfcca98d9d1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996fd628ce053956836db9e8e1756f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd8e7e50c4d5ccf7b85813b94407018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3119922ef999fd84a3929f61d3c02cf7.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/acc290b44635265137fdf13146b6a6d9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42af8cdea9c5269c17aebb086afdd136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1a6ce0b35896c8a1c687a4376e71f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4fd1b64ad84ea4526aff135fa38968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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2024-03-27更新
|
368次组卷
|
2卷引用:内蒙古自治区包头市2024届高三一模数学(理)试题
5 . 设函数
.
(1)当
时,讨论
的单调性,并证明
;
(2)证明:①当
时,
;
②当
时,
,当
时,
;
③当
时,函数
存在唯一的零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/583f8821e1f933b3ae9ec56f82b20f60.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
(2)证明:①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0852d49275f8774ba92620d8af490c72.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a16e7c0a12d8b0be5194fc875a19065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221d0bf6c8cf0a1ff429f556a4d9cd5f.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51e2b8f615b2cc7eca7fda25efb507d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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2024高三·全国·专题练习
解题方法
6 . 已知椭圆
的长轴长为4,离心率为
,点
是椭圆上异于顶点的任意一点,过点
作椭圆的切线
,交
轴于点A,直线
过点
且垂直于
,交
轴于点
.
(1)求椭圆的方程;
(2)试判断以
为直径的圆能否过定点?若能,求出定点坐标;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求椭圆的方程;
(2)试判断以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2024-03-25更新
|
246次组卷
|
3卷引用:内蒙古自治区包头市2024届高三下学期适应性考试文科数学试题(二)
7 . 已知函数
.
(1)判断
的零点个数并说明理由;
(2)当
时,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b5efb4ba8af78864173cac998c7477.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e575edd9b3312cd2a9c0b625eb745f87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-03-21更新
|
472次组卷
|
3卷引用:内蒙古自治区包头市2024届高三下学期适应性考试理科数学试题(二)
内蒙古自治区包头市2024届高三下学期适应性考试理科数学试题(二)四川省成都市2024届高三下学期第二次诊断性检测文科数学试题(已下线)2023-2024学年高二下学期期中复习解答题压轴题十七大题型专练(1)
解题方法
8 . 已知双曲线
的左、右焦点分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
记以
为直径的圆与C的渐近线在第一象限交于点P,点Q为线段
与C的交点,O为坐标原点,且
,则C的离心率为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4454a5cb78a2629f81028047ad3aaca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ddb5ffda1ab2979afdbabe4b8ac4fc.png)
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2024-03-06更新
|
902次组卷
|
2卷引用:内蒙古自治区包头市2024届高三下学期适应性考试理科数学试题(二)
9 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,证明:在
上
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79d99210d95cea8aad823d04ada1032.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4f133cb14a3a1f0266da8cb55025ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32af76ca980c959bcde29df3a08aec3.png)
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2024-02-12更新
|
384次组卷
|
2卷引用:内蒙古包头市2024届高三上学期期末教学质量检测数学(理)试题
解题方法
10 . 已知
为锐角三角形,
,
,
,是角
,
,
分别所对的边,若
;且
,则
面积的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af30a92eda72d7b4daf2dc17c0c078af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-01-29更新
|
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5卷引用:内蒙古包头市2024届高三上学期期末教学质量检测数学(理)试题
内蒙古包头市2024届高三上学期期末教学质量检测数学(理)试题内蒙古自治区锡林郭勒盟2023-2024学年高三上学期1月期末教学质量检测理科数学试题内蒙古自治区锡林郭勒盟2023-2024学年高三上学期1月期末教学质量检测文科数学试题(已下线)考点13 正弦定理及应用 --2024届高考数学考点总动员【练】(已下线)第一次月考填空题压轴题十四大题型专练-举一反三系列