1 . 已知抛物线
经过点
,其焦点为
.
(1)求抛物线
的方程;
(2)设点
在抛物线
上,试问在直线
上是否存在点
,使得四边形
是平行四边形?若存在,求出点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfb23a9e07213cb76990dbedfc7feca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](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/915214095e7786e305562acf3c083026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72488f87869909ff96685f1e78ddc64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
名校
解题方法
2 . 抛物线
的焦点为
,其准线与
轴的交点为
,过点
作直线与此抛物线交于
,
两点,若
,则
( )
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d56fffeca88040c5e70b1d240bcac66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97597c62ffed03dab6eb6381cd4e665d.png)
A.3 | B.4 | C.5 | D.6 |
您最近一年使用:0次
2022-08-13更新
|
1450次组卷
|
7卷引用:贵州省贵阳市白云区第二高级中学2021-2022学年高二下学期期末联考数学(理)试题
贵州省贵阳市白云区第二高级中学2021-2022学年高二下学期期末联考数学(理)试题(已下线)第三章 圆锥曲线的方程(A卷·知识通关练)(5)(已下线)第03讲 抛物线(练)(已下线)专题9-4 抛物线性质应用归类-2贵州省贵阳市白云区第二高级中学2021-2022学年高二下学期期末联考数学(文)试题(已下线)高二上学期期中考试选择题压轴题50题专练-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)江西省乐平中学2022-2023学年高二下学期3月月考数学试题
名校
3 . 已知抛物线
经过点
,其焦点为
.
(1)求抛物线
的方程;
(2)设点
在抛物线
上,试问在直线
上是否存在点
,使得四边形
是平行四边形?若存在,求出点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfb23a9e07213cb76990dbedfc7feca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](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/915214095e7786e305562acf3c083026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72488f87869909ff96685f1e78ddc64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2022-08-12更新
|
1704次组卷
|
4卷引用:2023版 北师大版(2019) 选修第一册 突围者 第二章 专项拓展训练4 圆锥曲线中的探索性问题
2023版 北师大版(2019) 选修第一册 突围者 第二章 专项拓展训练4 圆锥曲线中的探索性问题抛物线的综合问题(已下线)专题26 求动点轨迹方程 微点3 待定系数法求动点的轨迹方程黑龙江省鹤岗市第一中学2022-2023学年高二上学期期中数学试题
4 . 如图,已知点
为抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
的焦点.过点F的直线交抛物线于A,B两点,点A在第一象限,点C在抛物线上,使得
的重心G在x轴上,直线
交x轴于点Q,且Q在点F的右侧,记
,
的面积分别为
,
.
![](https://img.xkw.com/dksih/QBM/2022/8/4/3037105577558016/3042714526654464/STEM/bf67e370a34b401f8523c86995aff737.png?resizew=185)
(1)求p的值及抛物线的准线方程;
(2)设A点纵坐标为
,求
关于t的函数关系式;
(3)求
的最小值及此时点G的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75de1947893e5c7a4d98d4458398fd6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7572ecc467c061ef71cf4486ec63ec3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ea53e1a6ae39dfaefbcd787a08b2ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://img.xkw.com/dksih/QBM/2022/8/4/3037105577558016/3042714526654464/STEM/bf67e370a34b401f8523c86995aff737.png?resizew=185)
(1)求p的值及抛物线的准线方程;
(2)设A点纵坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dffc8f00c4e34f8113ba86977c3136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
2022-08-12更新
|
879次组卷
|
4卷引用:上海市松江一中2022届高三下学期3月阶段测试数学试题
上海市松江一中2022届高三下学期3月阶段测试数学试题(已下线)第15讲 抛物线 - 1(已下线)专题3.13 直线与抛物线的位置关系-重难点题型精讲-2022-2023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)黑龙江省鹤岗市第一中学2022-2023学年高二上学期期中数学试题
5 . 已知抛物线
,点
为直线
上一动点,过点
作直线
与
分别切于点
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61557cca4e2f97defc23aeb18b13f724.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03df57efff473b3cfeb8503796b7d6b6.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/61557cca4e2f97defc23aeb18b13f724.png)
您最近一年使用:0次
2022-08-09更新
|
881次组卷
|
4卷引用:专题3平面向量的数量积运算 (提升版)
解题方法
6 . 已知抛物线的顶点为坐标原点,焦点在坐标轴上,设
是抛物线上一点.
(1)求抛物线方程;
(2)若抛物线的焦点在x轴上,过点M作两条直线
分别交抛物线于A,B两点(纵坐标均为非负数),若直线
与
的倾斜角互补,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192618493ca6110c91720699c3971d86.png)
(1)求抛物线方程;
(2)若抛物线的焦点在x轴上,过点M作两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/6a11cb104b04c4e6a1be700e81da279a.png)
您最近一年使用:0次
2022高三·全国·专题练习
7 . 已知椭圆
的长轴长为4,离心率为
,一动圆
过椭圆
右焦点
,且与直线
相切.
(1)求椭圆
的方程及动圆圆心轨迹
的方程;
(2)过
作两条互相垂直的直线,分别交椭圆
于
,
两点,交曲线
于
,
两点,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](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/99c6875d552e9fff3c7d655f3a59b166.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/23f3ffe7abc59e2f65d827c8eab8d36a.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/99393efa04579f3db5cf4f7e319f0440.png)
您最近一年使用:0次
8 . 已知点
,过点
且与y轴垂直的直线为
,
轴,交
于点N,直线l垂直平分FN,交
于点M.
(1)求点M的轨迹方程;
(2)记点M的轨迹为曲线E,直线AB与曲线E交于不同两点
,且
(m为常数),直线
与AB平行,且与曲线E相切,切点为C,试问
的面积是否为定值.若为定值,求出
的面积;若不是定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df80e89c0e6b9c87ec0af6e9209c23d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb178d38d11605fbc56438561887080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15ebdaa4b3e74f75ae6f2d3cdf9b6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(1)求点M的轨迹方程;
(2)记点M的轨迹为曲线E,直线AB与曲线E交于不同两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4daf40bad1cc89311930cce356672354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48219e54519428b022aa92ed5b9bc9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2022-07-17更新
|
2494次组卷
|
5卷引用:专题24 圆锥曲线中的存在性、探索性问题 微点3 圆锥曲线中的存在性、探索性问题综合训练
(已下线)专题24 圆锥曲线中的存在性、探索性问题 微点3 圆锥曲线中的存在性、探索性问题综合训练(已下线)专题26 求动点轨迹方程 微点2 定义法求动点的轨迹方程(已下线)专题3.16 圆锥曲线中的定点、定值、定直线问题大题专项训练(30道)-2022-2023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)百校联盟2018届TOP20一月联考(全国Ⅰ卷)理科数学试题(已下线)第32节 圆锥曲线中的定点定值问题
9 . 已知抛物线
上的点
到焦点
的距离等于圆
的半径.
(1)求抛物线
的方程;
(2)过点
作两条互相垂直的直线
与
,直线
交
于
,
两点,直线
交
于
,
两点,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1ca65e3b183f5d69591f29df2cf9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9bd21c02aa54a27559b8673e327d42.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/2e9b0f5f44abbc6544a2f672b025b013.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/3f6f17bc385bafb37e8f964e5eb99cd0.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/96198405db093eb43952282a69332f92.png)
您最近一年使用:0次
2022-07-15更新
|
808次组卷
|
6卷引用:河南省开封市五县2021-2022学年高二下学期期末考试数学(文科)试题
河南省开封市五县2021-2022学年高二下学期期末考试数学(文科)试题河南省商丘市一高2021-2022学年下学期高二期末考试文科数学试题(已下线)【题型分类归纳】2022-2023学年高二数学同步讲与练(空间向量与立体几何、直线与圆、圆锥曲线、数列)(已下线)专题3.13 直线与抛物线的位置关系-重难点题型精讲-2022-2023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)(已下线)专题3.15 圆锥曲线中的面积问题大题专项训练(30道)-2022-2023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)江苏省徐州市睢宁县第一中学2022-2023学年高二上学期10月月考数学试题
名校
10 . 已知抛物线
过点
,过点
的直线交抛物线于
,
两点,点
在点
右侧,若
为焦点,直线
,
分别交抛物线于
,
两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266504a4bd910b292c74765dc9772f62.png)
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4卷引用:重庆市南开中学校2021-2022学年高二下学期期末数学试题
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