1 . 已知双曲线:
的一个焦点与抛物线
:
的焦点重合.
(1)求抛物线
的方程;
(2)若直线
:
交抛物线
于A、B两点,O为原点,求证:以
为直径的圆经过原点O.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b9c7b568fd86cc7c93975b8a74589a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ced1128ab10d92185ee554a640f2e93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2023-11-02更新
|
2451次组卷
|
12卷引用:山东省泰安市新泰市第一中学东校2023-2024学年高二上学期冬季学科竞赛数学试题
山东省泰安市新泰市第一中学东校2023-2024学年高二上学期冬季学科竞赛数学试题云南省昆明市云南师范大学附属中学2023-2024学年高二上学期期中考试数学试题江苏省扬州市扬州中学2023-2024学年高二上学期期中考试数学试题吉林省长春吉大附中实验学校2023-2024学年高二上学期期中考试试题黑龙江省齐齐哈尔市第八中学校2023-2024学年高二上学期12月月考数学试题吉林省辽源市田家炳高级中学校2023-2024学年高二上学期12月月考数学试题福建省福州市福清西山学校2023-2024学年高二上学期12月月考数学试题(已下线)第三章 圆锥曲线的方程【单元基础卷】-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)3.3.2 抛物线的简单的几何性质(重难点突破)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)第5讲:定点、定值、定直线问题【练】(已下线)通关练17 抛物线8考点精练(3)(已下线)专题26 直线与圆锥曲线的位置关系5种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)
2 . 已知函数
.
(1)若曲线
在点
处与直线
相切,求
的值;
(2)若函数
有两个零点
,试判断
的符号,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb13207f3d5ea73c3efa9452af764de.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a026fe55f6e9fe8ebefa239d56d9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90baac532eb4af70aca4e149fe59bfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c577ac4a86eab9d670c3de7d4f73d0e4.png)
您最近一年使用:0次
2017-02-08更新
|
553次组卷
|
3卷引用:2017届河南豫北名校联盟高三理上精英对抗赛数学试卷1
名校
3 . 如图,椭圆
(
)的离心率
,短轴的两个端点分别为B1、B2,焦点为F1、F2,四边形F1 B1F2 B2的内切圆半径为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572073853976576/1572073859776512/STEM/df666b46576e442f852686246cf058eb.png)
(1)求椭圆C的方程;
(2)过左焦点F1的直线交椭圆于M、N两点,交直线
于点P,设
,
,试证
为定值,并求出此定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374d3462754e846cbb0f7dd5fd28277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572073853976576/1572073859776512/STEM/df666b46576e442f852686246cf058eb.png)
(1)求椭圆C的方程;
(2)过左焦点F1的直线交椭圆于M、N两点,交直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305d76a955a792f249d9389c13161137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2275e890337c0c5b4e66de4e1a48e2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c544af590749e2ba41419fc3d53b78ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc9f0f081e55f02136f97614f94b36f.png)
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2016-12-03更新
|
468次组卷
|
2卷引用:浙江省镇海市镇海中学2017年高中数学竞赛模拟(二)试题
9-10高二下·黑龙江·期末
4 . 已知椭圆
过点
,且离心率
.
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/942052b9cbdd4a9fa8ad2b0d7d1f3110.png)
(Ⅰ)求椭圆方程;
(Ⅱ)若直线
与椭圆交于不同的两点
、
,且线段
的垂直平分线过定点
,求
的取值范围.
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/8ce15a373433487bb6753ddd3209fed4.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/69ae5024587b4d23a30f110bee47fbe2.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/5efcbacb9aea437d95f68e2a7117bd8a.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/942052b9cbdd4a9fa8ad2b0d7d1f3110.png)
(Ⅰ)求椭圆方程;
(Ⅱ)若直线
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/67f5912d46374f3b883a4f1487fb4de6.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/8e64dc7f52ea4d6ab889ebd444a29297.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/b1ec3990bc6744e79b2ade5b8bf8a6b7.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/b075ea9e030d43c98708e9b306ab9510.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/a5f078b9c15f421e97e67987b69e7955.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/bf13fc47f5a5481886340b68f2a970dd.png)
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