名校
解题方法
1 . 已知抛物线
的焦点为
为
上一点,且
.
(1)求抛物线
的方程;
(2)若直线
交抛物线
于
两点,且
(
为坐标原点),记直线
过定点
,证明:直线
过定点
,并求出
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6576531bce582abf03680ce41796ad88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56bbafa889700c6764ebc7fc1a42cd91.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/a528d113fdb2cded90a765015edd2774.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/44df59c8744bba67ed7805e920454634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51092551823722dfb7f69449b2f4698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a9bf6bda9363dbef5f6ff4bf6a5edf.png)
您最近一年使用:0次
2023-12-11更新
|
686次组卷
|
4卷引用:陕西省咸阳市永寿县中学2023-2024学年高三上学期调研模拟测试理科数学试卷
名校
解题方法
2 . 已知抛物线
的焦点
到双曲线
的渐近线的距离为
.
(1)求抛物线
的方程;
(2)过点
任意作互相垂直的两条直线
,
分别交曲线
于点A,B和M,N.设线段
,
的中点分别为P,Q,求证:直线
恒过一个定点.
![](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/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2024-01-16更新
|
1338次组卷
|
5卷引用:贵州省部分重点中学2024届高三上学期模拟数学试题
贵州省部分重点中学2024届高三上学期模拟数学试题广东省广州市第六中学2024届高三第三次调研数学试题(已下线)高考数学冲刺押题卷03(2024新题型)(已下线)题型24 5类圆锥曲线大题综合解题技巧(已下线)专题8.4 抛物线综合【八大题型】
名校
解题方法
3 . 在平面直角坐标系
中,顶点在原点,以坐标轴为对称轴的抛物线
经过点
.
(1)求
的方程;
(2)若
关于
轴对称,焦点为
,过点
且与
轴不垂直的直线
交
于
,
两点,直线
交
于另一点
,直线
交
于另一点
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5511a368692de27c58ec48ce968de4a4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081cd41dab0f2a8f84b0e9f1df4843fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.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/360496a4f5cc8a5faca5e089ae4f9531.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-10-20更新
|
641次组卷
|
9卷引用:河南省商丘市2022-2023学年高二下学期6月月考数学试题
河南省商丘市2022-2023学年高二下学期6月月考数学试题陕西省汉中市镇巴县2022-2023学年高二下学期期末理科数学试题江西省全南中学2022-2023学年高二下学期期末教学质量验收数学试题河南省商丘市部分学校2022-2023学年高二下学期6月摸底考试数学试题(已下线)第24讲 抛物线的简单几何性质6种常见考法归类(2)(已下线)专题3.7 直线与抛物线的位置关系【八大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)广东省惠州市泰雅实验高中2024届高三上学期第一次月考数学试题(已下线)第08讲:圆锥曲线(大题) (必刷7大考题+7大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)(已下线)2024届新高考数学信息卷5
解题方法
4 . 已知抛物线
和圆
交于
两点,且
,其中O为坐标原点.
(1)求
的方程.
(2)过
的焦点
且不与坐标轴平行的直线
与
交于
两点,
的中点为
,
的准线为
,且
,垂足为
.证明:直线
的斜率之积
为定值,并求该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471ebe959b8ff2bbabce1f0f09a36e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7919338a4271bfa738a67e7630441ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db36b4497b911bc047253b832ae01c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e775e1c7a1a275384e9ed500a3cadf4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436a0215888457c11878ec53937d6c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ec409450dfbbbb57adee4ca3472b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2024-01-20更新
|
289次组卷
|
5卷引用:广东省清远市2020-2021学年高二上学期期末数学试题
5 . 已知点
在抛物线
:
上,
、
为抛物线
上的两个动点,
不垂直于
轴,
为焦点,且
.
(1)求
的值,并证明
的垂直平分线过定点;
(2)设(1)中的定点为
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da61a8fc8f424929e9bf36622f1ca74f.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66c62178650010ead8cfdb2a00e2806.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)设(1)中的定点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
您最近一年使用:0次
名校
解题方法
6 . 已知
是抛物线
的焦点,抛物线上点A满足AF垂直于x轴,且
.
(1)求抛物线C的标准方程;
(2)
是该抛物线上的两点,
,求线段
的中点到
轴的距离;
(3)已知点
,直线
过点
与抛物线交于
,
两个不同的点
均与点H不重合
,设直线
,
的斜率分别为
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d653eb1ea0106e5bb146dae2e4e0e34f.png)
(1)求抛物线C的标准方程;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ea647b776699a17f47fae1f25dc158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c627ad9fd5be5001321b0ca8ce941e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28c6ce14821fdbe53aca895e52ab1e7.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/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a8588dc60a543ad70d6bc0d263dbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef1f7b9adab87736321e30949a4d668.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/b4757181824e15e0f21e5bdd55448783.png)
您最近一年使用:0次
7 . 已知点
在抛物线
:
上,点F为
的焦点,且
.过点F的直线
与
及圆
依次相交于点A,B,C,D,如图.
的方程及点M的坐标;
(2)证明:
为定值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c26e2b0282402f4c622bb7b36a1a637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea1ce7588f88b39746159233be9cd82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16e0a493a582d7a2c69308f411c677b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9299cbb1124e6984eebd37894187f5ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f7058b04346688b7635310597e6ece.png)
您最近一年使用:0次
8 . 曲线
,第一象限内点
在
上,
的纵坐标为
.
(1)若
到准线距离为3,求
;
(2)设
为坐标原点,
,
,
为
上异于
的两点,且直线
与
斜率乘积为4.证明:直线
过定点;
(3)直线
,令
是第一象限
上异于
的一点,直线
交
于
,
是
在
上的投影,若点
满足“对于任意
都有
”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32e577ae1f4449efbd64c1199efe7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)直线
![](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/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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9 . 在平面直角坐标系中,已知抛物线
的焦点
与椭圆
的一个焦点重合,
是抛物线
上位于
轴两侧不对称的两动点,且
.
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dead7389238047959fc220801fd58caa.png)
①求出点坐标;
②当为
的内心时,求
重心的坐标.
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10 . 已知抛物线
为E上位于第一象限的一点,点P到E的准线的距离为5.
(1)求E的标准方程;
(2)设O为坐标原点,F为E的焦点,A,B为E上异于P的两点,且直线
与
斜率乘积为
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e222cb19a044c842eea458e8b8ec8f39.png)
(1)求E的标准方程;
(2)设O为坐标原点,F为E的焦点,A,B为E上异于P的两点,且直线
![](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/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2023-12-27更新
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4卷引用:海南省海口市海口中学2024届高三上学期第四次月考数学试题
海南省海口市海口中学2024届高三上学期第四次月考数学试题宁夏石嘴山市平罗中学2023-2024学年高二上学期期末数学试题(已下线)【一题多解】定点最值 代数几何(已下线)专题18 圆锥曲线高频压轴解答题(16大核心考点)(讲义)-2