解题方法
1 . 已知
为坐标原点,过点
的直线
与抛物线C:
交于
两点.
(1)证明:
;
(2)若
与坐标轴不平行,且
关于
轴的对称点为
,圆
:
,证明:直线
恒与圆
相交.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894c9c9109361963cf5196f89c1f2d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2022-12-31更新
|
187次组卷
|
3卷引用:陕西省安康市2022-2023学年高二下学期开学摸底考试文科数学试题
解题方法
2 . 已知函数
.
(1)求函数
的极值;
(2)证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef278509c5a53f41402ecf1785c883e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec5f0a10e28f80b2f5b1a40afa72494.png)
您最近一年使用:0次
3 . 已知函数
.
(1)若函数
在
处取得极值,求
的单调区间;
(2)若
,证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645c993c73304807a69db775a37f7bc1.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/317f9ce5d2b8b00117904ec6bd50ddc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67cbb47080afc6ed336950a0fc2b04cc.png)
您最近一年使用:0次
4 . 已知抛物线
,直线l经过抛物线C的焦点,且垂直于抛物线C的对称轴,直线l与抛物线C交于M,N两点,且
.
(1)求抛物线C的方程;
(2)已知点
,直线
与抛物线C相交于不同的两点A,B,设直线PA与直线PB的斜率分别为
和
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e00ad067ceaf3a8c0452e5cd52a506.png)
(1)求抛物线C的方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46ec2efa825875cd0938691f5547aee.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/6b881044b5c73db6fcce110525741b02.png)
您最近一年使用:0次
2022-07-02更新
|
4378次组卷
|
5卷引用:陕西省西安市阎良区2020-2021学年高二上学期期末文科数学试题
陕西省西安市阎良区2020-2021学年高二上学期期末文科数学试题(已下线)专题4 齐次化妙解圆锥曲线问题 微点1 齐次化妙解圆锥曲线问题(已下线)第10讲 高考难点突破二:圆锥曲线的综合问题(定值问题) (精讲)河南省驻马店市上蔡县衡水实验中学2022-2023学年高三上学期8月月考数学(文)试题(已下线)专题21 抛物线的焦点弦 微点1 抛物线的焦点弦常用结论及其应用
5 . 设抛物线
的焦点为
,点
是抛物线
上一点,且
.
(1)求抛物线
的方程;
(2)若
,
为抛物线
上异于点
的两点,且
,设直线
的方程为
,点
,
到直线
的距离分别为
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265c1916c8cf891c8b0cc310ae46c940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c35531b38d16272285f5b84c713dc5.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.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/83640592853a53872d7af69c0cffc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d82ad901e081955d3ab45468d6811d6.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/1b6280959e386eed67ce5d6f8da5dcdc.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/18f0281e6bbdbe08beeccb55adf84536.png)
您最近一年使用:0次
名校
解题方法
6 . 已知椭圆C:
的离心率
,且圆
过椭圆C的上、下顶点.
(1)求椭圆C的方程;
(2)若直线l的斜率为
,且直线l与椭圆C相交于P,Q两点,点P关于原点的对称点为E,点
是椭圆C上一点,若直线AE与AQ的斜率分别为
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
(1)求椭圆C的方程;
(2)若直线l的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff20ed0b3544f29756b858798054a3d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e29652da1247c6c90a5545b41327729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7b9b8ca9a673b31f80b38ba2440d72.png)
您最近一年使用:0次
2022-07-24更新
|
2782次组卷
|
11卷引用:陕西省商洛市柞水中学2023-2024学年高二上学期期中质量检测数学试题
陕西省商洛市柞水中学2023-2024学年高二上学期期中质量检测数学试题河南省濮阳市油田第二高级中学2022届高三下学期数学(文科)考试试题广东省鹤山市鹤华中学2023届高三上学期开学摸底数学试题北京市景山学校2023届高三上学期开学摸底测试数学试题甘肃省张掖市2022-2023学年高三上学期第一次诊断考试数学(文)试题(已下线)专题22 圆锥曲线中的定点、定值、定直线问题 微点4 圆锥曲线中的定点、定值、定直线综合训练黑龙江省牡丹江市第三高级中学2022-2023学年高二上学期期中数学试题云南省大理白族自治州民族中学2022-2023学年高二下学期3月月考数学试题云南省玉溪第一中学2022-2023学年高二上学期第一次月考数学试题(已下线)第3章 圆锥曲线的方程单元测试基础卷-2023-2024学年高二上学期数学人教A版(2019)选择性必修第一册黑龙江省哈尔滨市第三中学校2023-2024学年高二下学期寒假验收考试数学试卷
解题方法
7 . 已知
且
.
(1)若
,求证:
;
(2)若当
时,曲线
与直线
有且只有两个交点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc33ef35f7cfca753e8614662b65a87.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7144b033af7d4a054a465982e5a3a85a.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ec33f7b7d2c0ccab9a3910e0a1b037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
您最近一年使用:0次
解题方法
8 . 已知函数
.
(1)若曲线
在点
处的切线方程为
,求
的值;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28426895da8037f75284732d25f95e97.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8e198436b70d9ac17be00c5cb59919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
您最近一年使用:0次
2022-05-07更新
|
193次组卷
|
2卷引用:陕西省西安市鄠邑区2021-2022学年高二下学期期中理科数学试题
9 . 已知椭圆
的离心率为
,椭圆
,椭圆
的切线
交椭圆
于M、N两点,切点为Q.
(1)求椭圆
的标准方程;
(2)求证:点Q是线段
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7b3883cbd340405a5f7aacc644aaf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c814ea7f841eae18168871f91dd6913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
(2)求证:点Q是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
解题方法
10 . 已知函数
.
(1)求函数
的单调区间;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bc03d4c05bafc41af16fd0057b0cada.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e982299c9ba12d5542b689496b274b9e.png)
您最近一年使用:0次
2023-01-11更新
|
941次组卷
|
5卷引用:陕西省渭南市韩城市新蕾中学2021-2022学年高二上学期第四次月考文科数学试题
陕西省渭南市韩城市新蕾中学2021-2022学年高二上学期第四次月考文科数学试题陕西省铜川阳光中学2021-2022学年高二上学期期末文科数学试题(已下线)第五章 一元函数的导数及其应用 讲核心 03(已下线)第六章 导数及其应用(A卷·知识通关练)(5)(已下线)拓展五:利用导数证明不等式的9种方法总结-【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)