名校
解题方法
1 . 选用恰当的证明方法;解决下列问题.
(1)
为实数,且
,证明:两个一元二次方程
,
中至少有一个方程有两个不相等的实数根.
(2)已知:
,且
,求证:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1476efe1fd8970d815af8a6e62d454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341f6b48e2c616585ed9bd7dbb9c8728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3ce04492780c4d40fab17aa28d3755.png)
(2)已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c96a416540d6d2c2570c7106f5e0492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03f1c0c0618a585e86afc523bd523e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356bc29ee1bc3f046d9a7b2804c77cf9.png)
您最近一年使用:0次
2023-10-14更新
|
98次组卷
|
2卷引用:江西省上饶市广丰中学2023-2024学年高一上学期10月月考数学试题
名校
解题方法
2 . 已知椭圆
的右焦点
恰为抛物线
的焦点,过点
且与
轴垂直的直线截抛物线、椭圆所得的弦长之比为
.
(1)求
的值;
(2)已知
为直线
上任一点,
分别为椭圆的上、下顶点,设直线
与椭圆的另一交点分别为
,求证:直线
过定点.并求出该定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b24214f111f7c6d2b64e53ad970438b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af31a8d791f28399fc13be3250136dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
3 . 已知函数
.
(1)定义
,其中
且
,求
;
(2)对于(2)中的
,求证:对于任意
都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2170843053c6714cd98f5a6ad4a0334a.png)
(1)定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8803ba7ef10e3204d74a86578d0793f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)对于(2)中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae373255bbe6f55879762cb4098d9094.png)
您最近一年使用:0次
解题方法
4 . 已知双曲线C:
的右顶点为
,且双曲线C的一条渐近线恰好与直线
垂直.
(1)求双曲线C的方程
(2)若直线
:
与双曲线C的右支交于A,B两点,点F为双曲线C的右焦点,点D在双曲线C上,且
轴.求证:直线
过点F.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb374fd349306abf2f784b6a28d93a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
(1)求双曲线C的方程
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303094682b317daea83be885d1c7ff4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d3a0273d1f3046dfad2086d0df56c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
2023-11-26更新
|
619次组卷
|
3卷引用:江西省上饶市广信二中2023-2024学年高二上学期期中数学试题
名校
解题方法
5 . 已知函数
,
,
为其导函数.函数
在其定义域
内有零点
.
(1)求实数a的取值范围;
(2)设函数
,求证:对任意的
且
,
.
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53a190256f3683315a8b60811b767b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.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/0109d06b8be2e402b5ffbb0aeb501009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)求实数a的取值范围;
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65760052439f87abfdb77c5e8898ee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb3ba497136e83ffa942f09c14b5b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f28c1416289e753d70b6e6c0b7e836e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac677478518ff0b76c3ab510ce625354.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee37a9ca13d5790552afc8facdd28f67.png)
您最近一年使用:0次
2023-11-08更新
|
486次组卷
|
2卷引用:江西省抚州市乐安县第二中学2024届高三上学期11月期中检测数学试题
名校
解题方法
6 . 固定项链的两端,在重力的作用下项链所形成的曲线是悬链线
年,莱布尼茨等得出悬链线的方程为
,其中
为参数.当
时,该表达式就是双曲余弦函数,记为
,悬链线的原理常运用于悬索桥、架空电缆、双曲拱桥、拱坝等工程.已知三角函数满足性质:①导数:
;②二倍角公式:
;③平方关系:
.定义双曲正弦函数为
.
(1)写出
,
具有的类似于题中①、②、③的一个性质,并证明该性质;
(2)任意
,恒有
成立,求实数
的取值范围;
(3)正项数列
满足
,
,是否存在实数
,使得
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a7e0115ce78639910150e39fdbdb0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07f8015f0a035e80a166092be0b7318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a7c1d3681898e25187a896aeb0c8c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8bce35b539fdf365e9089750d4d152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32eac4b7f177c041219fab18de973c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af7ca3fcd9a43d520ed650b80ef2dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0718c04bdf70989bcc90b902671a692.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53b8e0108664bf39aa302570457199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7c627427318b62d977ff7a86c2cb5.png)
(2)任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68fd5f6e28316a932db1494deac24b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19bf566cd9dd81916f53ed33248197c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f816db73b759d7de72b0bd43ba39f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecf3a1fecf89a37a677393d0bfe27b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/805dabba8d859d870a1dfaaa9d97de41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-06-02更新
|
440次组卷
|
2卷引用:江西省萍乡市2024届高三二模考试数学试卷
名校
解题方法
7 . 在平面直角坐标系
中,顶点在原点,以坐标轴为对称轴的抛物线
经过点
.
(1)求
的方程;
(2)若
关于
轴对称,焦点为
,过点
且与
轴不垂直的直线
交
于
,
两点,直线
交
于另一点
,直线
交
于另一点
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5511a368692de27c58ec48ce968de4a4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081cd41dab0f2a8f84b0e9f1df4843fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.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/360496a4f5cc8a5faca5e089ae4f9531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-10-20更新
|
641次组卷
|
9卷引用:江西省全南中学2022-2023学年高二下学期期末教学质量验收数学试题
江西省全南中学2022-2023学年高二下学期期末教学质量验收数学试题河南省商丘市2022-2023学年高二下学期6月月考数学试题陕西省汉中市镇巴县2022-2023学年高二下学期期末理科数学试题河南省商丘市部分学校2022-2023学年高二下学期6月摸底考试数学试题(已下线)第24讲 抛物线的简单几何性质6种常见考法归类(2)(已下线)专题3.7 直线与抛物线的位置关系【八大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)广东省惠州市泰雅实验高中2024届高三上学期第一次月考数学试题(已下线)第08讲:圆锥曲线(大题) (必刷7大考题+7大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)(已下线)2024届新高考数学信息卷5
解题方法
8 . 已知函数
和
.
(1)求函数
的极值;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe3c7a1c096f5ed99b91d40d71d3ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40900c80cf73306e135214acf5db093f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561800aa679a45da4dbe0e323de1fd59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
您最近一年使用:0次
2023-10-16更新
|
386次组卷
|
2卷引用:江西省宜春市上高县2024届高三上学期11月月考数学试题
名校
解题方法
9 . 已知动圆P过点
且与直线
相切,圆心P的轨迹为曲线C.
(1)求曲线C的方程;
(2)若A,B是曲线C上的两个点,且直线AB过
的外心,其中O为坐标原点,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb747d2028ebe5ea8337800e4c3f5fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32ae4ac252986a77c07b980d375a3fd.png)
(1)求曲线C的方程;
(2)若A,B是曲线C上的两个点,且直线AB过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-08-24更新
|
312次组卷
|
7卷引用:江西省九江市庐山市匡庐星瀚高级中学2023-2024学年高二上学期期中数学试题
江西省九江市庐山市匡庐星瀚高级中学2023-2024学年高二上学期期中数学试题江西省鹰潭市2020-2021学年高二上学期期末数学(文)试题(已下线)3.3.2 抛物线的简单几何性质(6大题型)精讲-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)(已下线)第3章 圆锥曲线与方程单元检测(提优卷)-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)湖南省长沙市长郡中学2019-2020学年高二上学期期中数学试题新疆维吾尔自治区昌吉回族自治州2022-2023学年高二上学期11月期中质量检测数学试题四川省泸州市泸县第四中学2023-2024学年高二上学期期末数学试题
10 . 已知椭圆
的左、右焦点分别为
,
,长轴的左、右端点分别为
,
,短轴的上、下端点分别为
,
,设四边形
的面积为S,且
.
(1)求
,
的值;
(2)过点
作直线
与
交于
,
两点(点
在
轴上方),求证:直线
与直线
的交点
在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6939353e2387477b4149848a2818e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc42863b519330c6756b8927e868e09d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/8455657dde27aabe6adb7b188e031c11.png)
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2023-12-15更新
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2卷引用:江西省宜春市丰城拖船中学2023-2024学年高二上学期期中数学试题