名校
解题方法
1 . 已知平面内一动点
到定点
的距离比它到
轴的距离多1.
(1)求
点的轨迹方程
;
(2)过点
作直线
与曲线
交于
(
点在
点左侧),求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2347bec7975dab2b8bce2fd19b1237d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0643ae2942b740d78b7ace0d4e630ac.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/01c74a907dda6bb7d9d56d009d9df253.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/7cf4d0c1407ae02de1b899c410e2211f.png)
您最近一年使用:0次
2023-01-09更新
|
962次组卷
|
5卷引用:广东省五校(华附,省实,深中,广雅,六中)2022-2023学年高二上学期期末联考数学试题
名校
解题方法
2 . 已知圆的方程
,
,
,抛物线过
两点,且以圆的切线为准线.
(1)求抛物线焦点的轨迹C的方程;
(2)已知
, 设x轴上一定点
, 过T的直线交轨迹C于
两点(直线
与
轴不重合),求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54329a84abb204cecb237b2bf2ff2bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求抛物线焦点的轨迹C的方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c153027427477bcd0a7228b14ce96cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf5077ae09443a75fb8301841116a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b800af3d8614f3f30eefa7de8d0b581f.png)
您最近一年使用:0次
2024-02-03更新
|
900次组卷
|
3卷引用:四川省成都市2023-2024学年高二上学期期末校级调研联考数学试题
2023高一·全国·专题练习
名校
解题方法
3 . 已知圆
,动点
在
轴的右侧,
到
轴的距离比它到的圆心
的距离小1.
(1)求动点
的轨迹
的方程;
(2)过圆心
作直线
与轨迹
和圆
交于四个点,自上而下依次为A,M,N,B,若
,求
及直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0a5f7ad4ec354b98f1ec4b2356d368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/5134db8851564c05f18c129c75ddb3aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
4 . 已知点
与点
的距离比它到直线
的距离小
,若记点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)若直线
与曲线
相交于
两点,且
.求证直线
过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d1bed885fcb17bdcc978ed955677f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-05-05更新
|
2025次组卷
|
8卷引用:沪教版(2020) 选修第一册 单元训练 第2章 抛物线(B卷)
沪教版(2020) 选修第一册 单元训练 第2章 抛物线(B卷)(已下线)第14讲 抛物线-【暑假自学课】2022年新高二数学暑假精品课(苏教版2019选择性必修第一册)抛物线的综合问题江西省临川第一中学2022-2023学年高二上学期11月质量监测数学试题(已下线)3.3.2 抛物线的几何性质 (2)(已下线)3.3.2 抛物线的几何性质(2)(已下线)专题30 圆锥曲线的综合应用(针对训练)-2023年高考一轮复习精讲精练宝典(新高考专用)(已下线)第16讲 直线和圆锥曲线的位置关系(2)
5 . 已知抛物线
上的点
到焦点的距离为8,点
到
轴的距离为
.
(1)求抛物线的方程;
(2)取抛物线上一点
,过点
作两条斜率分别为
的直线与抛物线交于
两点,且
,则直线
是否经过一个定点?若经过定点,求出该点坐标,否则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8b928c60de1b77c0588a2503a7c565.png)
(1)求抛物线的方程;
(2)取抛物线上一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594d4b99d4c5c90fc2e8010cc198551d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a690a05dc243e3c6736a6de514106ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2024-01-12更新
|
873次组卷
|
3卷引用:云南省昆明市官渡区2023-2024学年高二上学期1月期末学业水平考试数学试题
名校
解题方法
6 . 已知曲线M上的任意一点到点
的距离比它到直线
的距离小1.
(1)求曲线M的方程;
(2)设点
.若过点
的直线与曲线M交于B,C两点,求
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
(1)求曲线M的方程;
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3182f32cc4f57ff13155ada0231d606f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ea1f5bdd213c7c3a571b4c38850bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6818a98204f62c1b16699d26ca0c3f62.png)
您最近一年使用:0次
2023-01-04更新
|
911次组卷
|
5卷引用:北京市海淀区2022-2023学年高二上学期期末练习数学试题
北京市海淀区2022-2023学年高二上学期期末练习数学试题北京市中央民族大学附属中学2022-2023学年高二上学期期末数学试题(已下线)第三章 圆锥曲线的方程(易错必刷30题9种题型专项训练)-【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)期末真题必刷易错60题(32个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)(已下线)浙江省衢州、丽水、湖州三地市2022届高三(二模)数学试题变式题17-22
解题方法
7 . 已知
为抛物线
:
上的一个动点,
为
的焦点.
(1)当
时,求
的坐标;
(2)若点
的坐标为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ba3a6326dc83632fa772c1d34cbff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
8 . 已知抛物线
的焦点为
,直线
,点
,点
在抛物线
上,直线
与直线
交于点
,线段
的中点为
.
(1)求
的最小值;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f185d72f875b6ab532c1a5fc44fcb8fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b7a400f44ebe9b98090a34946af7f2c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467ed02ac3df7f54077250a50eb41af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次
2023-01-19更新
|
861次组卷
|
3卷引用:重庆市第八中学校2022-2023学年高二上学期期末数学试题
重庆市第八中学校2022-2023学年高二上学期期末数学试题江苏省如东高级中学、如东县第一高级中学、徐州中学、沭阳如东高级中学、宿迁市第一高级中学2023-2024学年高二上学期第二次阶段测试数学试卷(已下线)第七节 抛物线 第一课时 抛物线的定义、方程与性质 B素养提升卷
名校
解题方法
9 . 设抛物线
:
(
)的焦点为
,点
的坐标为
.已知点
是抛物线
上的动点,
的最小值为4.
(1)求抛物线
的方程:
(2)若直线
与
交于另一点
,经过点
和点
的直线与
交于另一点
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685e73f420b856ebf5eb4eda574a4fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508734095955bb96d52f37be4e681700.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa2dad9c6c0773c04cbf433d7b7dcc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583183429b6b31aa9742eefc67d3181.png)
您最近一年使用:0次
2023-09-09更新
|
841次组卷
|
4卷引用:辽宁省沈阳市东北育才学校2023-2024学年高二上学期第二次月考数学试题
辽宁省沈阳市东北育才学校2023-2024学年高二上学期第二次月考数学试题(已下线)专题08 抛物线的压轴题(5类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)福建省名校联盟2023届高三高考模拟考试4月数学试题(已下线)考点17 解析几何中的定点与定直线问题 2024届高考数学考点总动员
解题方法
10 . 在平面直角坐标系中,动点C到点
的距离与到直线
的距离相等.
(1)求动点C的轨迹方程;
(2)若直线
与动点C的轨迹交于P,Q两点,当
的面积为2时,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
(1)求动点C的轨迹方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adccd1dd14171c8c29d4a3836728c0f.png)
您最近一年使用:0次