1 . 已知点
皆为曲线C上点,P为曲线C上异于A,B的任意一点,且满足直线PA的斜率与直线PB的斜率之积为
.
(1)求曲线C的方程;
(2)若曲线
的右焦点为
,过
的直线
与曲线
交于
,求证:直线
与直线
斜率之和为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9c11cc36320090d0aaf0c621a63b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
(1)求曲线C的方程;
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65368687df4d7e3b9304e85ec4de354c.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/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c57b07f75e97d9f84718bd495ebcf4.png)
您最近一年使用:0次
2021-11-27更新
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483次组卷
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2卷引用:江西省南昌市八一中学、洪都中学等4校2021-2022学年高二上学期期中联考数学(文)试题
名校
解题方法
2 . 已知抛物线
, 点
是抛物线
上的点.
(1)求抛物线的方程及
的值;
(2)直线
与抛物线交于
两点,
,且
,求
的最小值并证明直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188026eaa20f137d70e994415c8b32d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求抛物线的方程及
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1325c6fe42a9e5c04520d8a9bb6821b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79891395ddbe2b31f3c91523176f7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4c0b1d1e4abf9057893bcd09e5940a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09821e8bfe3d8560cc814d3e210bbb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2021-11-23更新
|
485次组卷
|
4卷引用:江西省景德镇一中2022-2023学年高二(重点班)上学期期中考试数学试题
3 . 已知抛物线C: y2=2px (p>0),过抛物线的焦点F且垂直于x轴的直线交抛物线于不同的两点A,B, 且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179d7920ec6cd22f3a0cfa6738260153.png)
(1)求抛物线C的方程;
(2)若不经过坐标原点O的直线
与抛物线C相交于不同的两点M,N, 且满足
.证明直线
过x轴上一定点Q,并求出点Q的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179d7920ec6cd22f3a0cfa6738260153.png)
(1)求抛物线C的方程;
(2)若不经过坐标原点O的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328e4cc042e5177d41c17c3679164ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2021-11-21更新
|
360次组卷
|
2卷引用:江西省南昌市湾里区第一中学等六校2021-2022学年高二上学期期中联考数学(理)试题
4 . 已知点
皆为曲线C上点,P为曲线C上异于M,N的任意一点,且满足直线PM的斜率与直线PN的斜率之积为
.
(1)求曲线C的方程;
(2)若曲线上点
,经过曲线C右焦点
的直线
与曲线C交于
,
(异于
)两点,与直线
交于点
,设
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
的斜率分别为
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a3600dd6dacb0c8875075131f20001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)求曲线C的方程;
(2)若曲线上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afdf3c93dc3cba6e56a6c8fac12c8ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.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/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7298e9172c5139222535dd653549b9b6.png)
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名校
5 . 在平面直角坐标系
中,双曲线
的左右焦点分别为
,
,动点A为C右支上一点,右准线
与
轴交点为
.过点A作直线l的垂线交l于B,直线
交y轴于P,
.
(1)求C的方程;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112c938fab7625be9a7ad5021fa55d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.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/40460e97733a56b0b9963f8c641c47c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c429b542abf0ebee74a239b4857cf88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2d74904328122d5e0568fab4d88f08.png)
(1)求C的方程;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ea4d7be126de66b24fa394fdc050b6.png)
您最近一年使用:0次
2021-10-31更新
|
491次组卷
|
3卷引用:江西省宁冈中学2020-2021学年高二上学期期中考试数学(理)试题
江西省宁冈中学2020-2021学年高二上学期期中考试数学(理)试题江苏省南通市海安高级中学2021-2022学年高三上学期第一次月考数学试题(已下线)专题2 双曲线-学会解题之高三数学321训练体系【2022版】
解题方法
6 . 已知椭圆
(
)的焦距为4,其短轴的两个端点与长轴的一个端点构成正三角形.
(1)求椭圆
的标准方程;
(2)设
为椭圆
的左焦点,直线
,
为椭圆上任意一点,若点
到
的距离为
,点
到
的距离为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0778559e1601f19625786dc20304fe8.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be44077d42cfffece905b1af13e000.png)
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7 . 如图所示,在平面直角坐标系
中,P是不在x轴上的一个动点,过点P可作抛物线
的两条切线,两切点A、B的连线与
垂直.设直线
与直线
与x轴的交点分别为Q、R.
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815037014687744/2815804218966016/STEM/6577450b-894a-4048-a6d1-ee81f24bcd36.png?resizew=234)
(1)证明:R是一个定点;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815037014687744/2815804218966016/STEM/6577450b-894a-4048-a6d1-ee81f24bcd36.png?resizew=234)
(1)证明:R是一个定点;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50c707d0350c121c6a611db39a5e85d.png)
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2021-09-25更新
|
624次组卷
|
3卷引用:江西省永新中学2021-2022学年高二上学期期中考试数学(理)试题
名校
解题方法
8 . 已知抛物线
的准线与
轴的交点为
.
(1)求
的方程;
(2)若过点
的直线
与抛物线
交于
,
两点.求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311497849126f1aaf1da0ec75602eabf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a0d4c22734cac795de1e5c5fbefa87.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca007c9790f9716d1b36fa11b4b50809.png)
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2021-07-31更新
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3490次组卷
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18卷引用:江西吉安市永新县禾川中学2022-2023学年高二下学期期中数学试题
江西吉安市永新县禾川中学2022-2023学年高二下学期期中数学试题湖南省邵阳市第二中学2022-2023学年高二上学期期中数学试题江西省上饶市广丰区重点高中2022-2023学年高二上学期第三次月考数学试题四川省南充市2020-2021学年高二下学期期末考试数学(理)试题四川省南充市2020-2021学年高二下学期期末数学文科试题(已下线)第3章 圆锥曲线与方程(章末测试基础卷)-2021-2022学年高二数学同步单元测试定心卷(苏教版2019选择性必修第一册)(已下线)第3章 圆锥曲线与方程 单元综合检测(基础过关)(单元培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)试卷10(第1章-3.3抛物线)-2021-2022学年高二数学易错题、精典题滚动训练(苏教版2019选择性必修第一册)(已下线)3.3抛物线(专题强化卷)-2021-2022学年高二数学课堂精选(人教A版2019选择性必修第一册)2023版 北师大版(2019) 选修第一册 名师精选卷 第一、二、三章滚动测试抛物线的综合问题江苏省淮安市钦工中学2022-2023学年高二上学期第一次月考数学试题山西省运城市景胜中学2022-2023学年高二上学期11月月考数学(B)试题(已下线)3.3.2 抛物线的几何性质 (2)(已下线)专题3.5 圆锥曲线的方程(能力提升卷)-2022-2023学年高二数学必考点分类集训系列(人教A版2019选择性必修第一册)河南省驻马店市确山县第一高级中学2022-2023学年高二上学期10月月考数学试题(已下线)3.3 抛物线(练习)-高二数学同步精品课堂(苏教版2019选择性必修第一册)四川省南充市阆中市川绵外国语学校2023-2024学年高二上学期期末复习数学试题(二)
名校
解题方法
9 . 已知椭圆
的标准方程为
,该椭圆经过点
,且离心率为
.
(1)求椭圆的标准方程;
(2)过椭圆
长轴上一点
(其中
为常数)作两条互相垂直的弦
,
.若弦
,
的中点分别为
,
,证明:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆的标准方程;
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8102596c8faea3cb1fc81ed48319ef10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/411461db15ee8086332c531e086c40c7.png)
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名校
解题方法
10 . 设抛物线
的焦点为
,过点
的动直线
与抛物线
交于
,
两点,当
在
上时,直线
的斜率为
.
(1)求抛物线的方程;
(2)在线段
上取点
,满足
,
,证明:点
总在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2b1410f44205658cea90e9ce85101c.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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(1)求抛物线的方程;
(2)在线段
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9卷引用:江西省鹰潭市贵溪市第一中学2022-2023学年高二下学期期中考试数学试题
江西省鹰潭市贵溪市第一中学2022-2023学年高二下学期期中考试数学试题(已下线)第11讲 拓展五:圆锥曲线的方程(定值问题)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)(已下线)通关练17 抛物线8考点精练(3)广东省肇庆市2021届高三下学期第三次统一检测数学试题广东省湛江市2021届高三下学期二模数学试题安徽师范大学附属中学2021届高三下学期5月最后一卷理科数学试题安徽省六安市第一中学2021届高三下学期适应性考试文科数学试题(已下线)专题3.9 抛物线的综合问题-2021年高考数学解答题挑战满分专项训练(新高考地区专用)(已下线)专题12 定比点差法及其应用 微点5 定比点差法综合训练