名校
1 . 在平面直角坐标系中,已知曲线
上的动点
到点
的距离与到直线
的距离相等.
(1)求曲线
的轨迹方程;
(2)过点
分别作射线
、
交曲线
于不同的两点
、
,且
.试探究直线
是否过定点?如果是,请求出该定点;如果不是,请说明理由.
![](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/50154acc6ad77c6c777fffe3a08afb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236a066876764d090523afe0ea734a21.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e584f799ea554fc5533925ead4672501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.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/ada25f76504c3fd1226da43c94cb4277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2019-12-10更新
|
1011次组卷
|
4卷引用:广东省广州市番禺区广东仲元中学2019-2020年高三上学期11月月考数学(理)试题
2 . 从抛物线
上各点向x轴作垂线,垂线段中点的轨迹为E.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/6d7c049f-17d1-469b-b3ca-19632fdcf0ec.png?resizew=140)
(1)求曲线E的方程;
(2)若直线
与曲线E相交于A,B两点,求证:
;
(3)若点F为曲线E的焦点,过点
的直线与曲线E交于M,N两点,直线
,
分别与曲线E交于C,D两点,设直线
,
斜率分别为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290a56449ad6dd65aec7525c94273f59.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/6d7c049f-17d1-469b-b3ca-19632fdcf0ec.png?resizew=140)
(1)求曲线E的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c966320d637cab491c67425ef1338966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(3)若点F为曲线E的焦点,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f579b73ca01978ec68e716f993bc3766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360496a4f5cc8a5faca5e089ae4f9531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41500510276fc1981cb71c449477226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a3f348a942d468f0d77c0dfbb41d87.png)
您最近一年使用:0次
名校
解题方法
3 . 已知抛物线
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
的焦点为
,直线
与
轴的交点为
,与抛物线
的交点为
,且
.
(1)求抛物线
的方程;
(2)过抛物线
上一点
作两条互相垂直的弦
和
,试问直线
是否过定点,若是,求出该定点;若不是,请说明理由.
![](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/b75ed10db4b9747a4b6d865b774f6b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de72a5190834f5dbe895596656c038b3.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbe02ff25cdb4dd7123e399ae69bcb7.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3043fea80050b76e52852abbd9ef6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c023f4b501684abd869b36d6e6c7f21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2020-03-05更新
|
725次组卷
|
5卷引用:四川省三台中学实验学校2019-2020学年高二12月月考数学(理)试题
四川省三台中学实验学校2019-2020学年高二12月月考数学(理)试题四川省泸县第二中学2020-2021学年高二上学期第一次月考数学(文)试题(已下线)专题30 圆锥曲线求过定点大题100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)(已下线)重难点突破08 圆锥曲线的垂直弦问题 (八大题型)陕西省咸阳市咸阳中学2024届高三上学期第四次阶段测试数学(理)试题
解题方法
4 . 已知抛物线
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
的焦点为
,点
在抛物线
上,且
.
(1)求抛物线
的方程;
(2)过抛物线
上一点
作两条互相垂直的弦
和
,试问直线
是否过定点,若是,求出该定点;若不是,请说明理由.
![](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/b75ed10db4b9747a4b6d865b774f6b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c237799868529ed26b5386639a07ca11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1584d07b1e2ddc64349f0f5940f3a3e.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3043fea80050b76e52852abbd9ef6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c023f4b501684abd869b36d6e6c7f21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
5 . 已知
是抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa96c86a9085aeb7a57ce955200f0c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
的焦点,
是抛物线上一点,且
.
(1)求抛物线
的方程;
(2)直线
与抛物线
交于
,
两点,若
(
为坐标原点),则直线
是否会过某个定点?若是,求出该定点坐标,若不是,说明理由.
![](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/aa96c86a9085aeb7a57ce955200f0c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75ed10db4b9747a4b6d865b774f6b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04342c55b1cded22d2751b521cb46733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09e8a127fffff3b4df40d85780ace8d.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef54adb0b01f212dd43fcea5913ce72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-02-27更新
|
1135次组卷
|
6卷引用:四川省雅安市2018-2019学年高二下学期期末数学试题
6 . 已知抛物线
和圆
,直线l经过定点
,依次交![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9e99a0a70ea0f6f25c0ae21eb909ba4.png)
于A,B,C,D四点,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b4c1c804155c0d296e2ca8e179cc1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65078fe544af7a5cfee4397fd720326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9e99a0a70ea0f6f25c0ae21eb909ba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768a10111ef3b919975a724d5d07350d.png)
A.2 | B.1 | C.![]() | D.![]() |
您最近一年使用:0次
7 . 已知直线
与抛物线
交于O和E两点,
.
(1)求抛物线C的方程;
(2)过点
的直线交抛物线C于A、B两点,P为
上一点,PA、PB与x轴相交于M、N两点,问M、N两点的横坐标的乘积
是否为定值?如果是定值,求出该定值,否则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66fdf25d7a12cd80f0df53d10e078c85.png)
(1)求抛物线C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c441c7e1d4bc397894cc8a6a169e0d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e495af4ffcb621f2b62810ab3f984ea.png)
您最近一年使用:0次
2020-02-18更新
|
417次组卷
|
2卷引用:四川省攀枝花市2019-2020学年高二上学期期末数学(文)试题
名校
8 . 已知点F是抛物线C:y2=2px(p>0)的焦点,若点P(x0,4)在抛物线C上,且
.
(1)求抛物线C的方程;
(2)动直线l:x=my+1(m
R)与抛物线C相交于A,B两点,问:在x轴上是否存在定点D(t,0)(其中t≠0),使得kAD+kBD=0,(kAD,kBD分别为直线AD,BD的斜率)若存在,求出点D的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf7f16886647f47add4df8c7de6c45f2.png)
(1)求抛物线C的方程;
(2)动直线l:x=my+1(m
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02d44492b51b0e08208fdc0d1707025.png)
您最近一年使用:0次
2020-01-23更新
|
509次组卷
|
4卷引用:四川省成都外国语学校2019-2020学年高二上学期12月月考数学(理)试题
名校
9 . 已知点P到直线y=﹣4的距离比点P到点A(0,1)的距离多3.
(1)求点P的轨迹方程;
(2)经过点Q(0,2)的动直线l与点P的轨轨交于M,N两点,是否存在定点R使得∠MRQ=∠NRQ?若存在,求出点R的坐标:若不存在,请说明理由.
(1)求点P的轨迹方程;
(2)经过点Q(0,2)的动直线l与点P的轨轨交于M,N两点,是否存在定点R使得∠MRQ=∠NRQ?若存在,求出点R的坐标:若不存在,请说明理由.
您最近一年使用:0次
2019-12-15更新
|
444次组卷
|
3卷引用:四川省泸县第四中学2019-2020学年高二下学期第一次在线月考数学(文)试题
名校
10 . 已知抛物线
:
的焦点为
,点
为
上异于顶点的任意一点,过
的直线
交
于另一点
,交
轴正半轴于点
,且有
,当点
的横坐标为3时,
为正三角形.
(1)求
的方程;
(2)若直线
,且
和
相切于点
,试问直线
是否过定点,若过定点,求出定点坐标;若不过定点,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/7f9e8449aad35c5d840a3395ea86df6d.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/9c55c0d80252139f9d0d26bd00eaaecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57474ed195bfcc985ed925d8e971d20a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88c9366bb209931c6b28353dbab9a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
2019-11-14更新
|
427次组卷
|
5卷引用:【全国百强校】四川省成都外国语学校2019届高三开学考试数学(理)试卷