名校
1 . 抛物线的光学性质是:位于抛物线焦点处的点光源发出的每一束光经抛物线反射后的反射线都与抛物线的对称轴平行.已知抛物线
的焦点为F,直线
,点P,Q分别是C,l上的动点,若Q在某个位置时,P仅存在唯一的位置使得
,则满足条件的所有
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4372448a67bdb8e24fbfa1cd556d711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9192fb2f70aa1e13f58d9644ad45506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
2022-12-31更新
|
1036次组卷
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7卷引用:辽宁省大连市2022-2023学年高二上学期期末数学试题
辽宁省大连市2022-2023学年高二上学期期末数学试题(已下线)专题23 圆锥曲线中的压轴题(选填题)-2黑龙江哈尔滨市第一二二中学-202届高三一模数学试题安徽省合肥市肥东县综合高中2022-2023学年高二下学期第一次月考(2月)数学试题吉林省四平市第一高级中学2023-2024学年高二上学期第二次月考数学试题(已下线)期末真题必刷压轴60题(23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(人教A版2019选择性必修第一册)(已下线)第三章 圆锥曲线的方程(压轴必刷30题7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)
2 . 已知
是抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
内一动点,直线
过点
且与抛物线
相交于
两点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30ee8b98bd071f65863897db9cbacb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
A.![]() ![]() ![]() |
B.![]() ![]() |
C.当点![]() ![]() ![]() ![]() |
D.当点![]() ![]() ![]() ![]() ![]() |
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3 . 已知抛物线
的顶点在坐标原点,对称轴为坐标轴,且经过
三点中的两点.
(1)求抛物线
的方程;
(2)设
为坐标原点,
的焦点为
,过
的直线
与
交于
两点,过
的直线
与
交于
两点,点
都在第二象限,记直线
的倾斜角分别为
,且
.若直线
与直线
交于点
,不同于点
的点
满足
轴,当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
时,设
的面积分别为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3527271c0c60e9e5d747e4280da783f.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe56ede6bebd29d359e4f20af7fcaba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897a9dfb46e4d29358533e11e98d0dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8b39681e016b146ed9ea7d912e8e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/ff5ec3aef789fc1412ff76b510b48018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b622ac356325584b63fc96af7bab4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a644f5395815cbf1f01dcb60d288abdc.png)
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23-24高二上·全国·课后作业
解题方法
4 . 如图,
是抛物线
对称轴上一点,过点M作抛物线的弦AB,交抛物线于A,B.
,求弦AB中点的轨迹方程;
(2)过点M作抛物线的另一条弦CD,若AD与y轴交于点E,连接ME,BC,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbfc5253a678d786c9a8091fff43729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
(2)过点M作抛物线的另一条弦CD,若AD与y轴交于点E,连接ME,BC,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/490111e9e5aefb170410f0501134d22e.png)
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解题方法
5 . 已知抛物线
的焦点为
,其准线与
轴的交点为
.直线
与
没有公共点,直线
经过点
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed4c118054df599726d1351465645ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a388a8e291afb1c37d0faee69dee2a.png)
A.![]() | B.![]() ![]() |
C.以![]() ![]() | D.![]() ![]() |
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名校
6 . 已知抛物线
的准线为
,点
在
上,且
到
的距离与
到原点
的距离相等.
(1)求
的方程;
(2)
是
上异于原点
的四个动点,且
,若
,垂足分别为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5718c4cf68779669eb41ff652b7e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559fc5975418f34d3695f67b2ea45092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff8bb8c02ca9652683a42b48b5a8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
2022-03-31更新
|
1088次组卷
|
4卷引用:山东省聊城市2022届高三一模数学试题
山东省聊城市2022届高三一模数学试题(已下线)专题二十四 抛物线(已下线)秘籍06 解析几何-备战2022年高考数学抢分秘籍(新高考专用)湖北省孝感市应城市第一高级中学2021-2022学年高三上学期8月热身考试数学试题
7 . 已知圆
与直线
相切,与圆
交于
两点,且
为圆
的直径,圆心
的轨迹为
.
(1)求轨迹
的方程;
(2)设点
是
上不同的两点,且直线
的斜率均为
为
轴上一动点,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2917b590f29d4130e0fc081a387b2c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2a2d98a9ae3e6d58c9bbcb5146a91c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135566c18cd3b338e9ec141f1b14789b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bcea830a5f206033d07d35e1fd05378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a09efeb6f23d0aef2b89ddce307da8.png)
您最近一年使用:0次
2023-12-20更新
|
527次组卷
|
2卷引用:云南省北京教能教育集团(昆明艺卓中学)2023-2024学年高二上学期12月月考数学试题
8 . 过圆锥曲线的焦点且与焦点所在的对称轴垂直的弦被称为该圆锥曲线的通径,清代数学家明安图在《割圆密率捷法》中,也称圆的直径为通径.已知圆
的一条通径与抛物线
的通径恰好构成一个正方形的一组邻边,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbab00ce6d1aeb12ddbbb65a8c69fa3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
A.![]() | B.1 | C.2 | D.4 |
您最近一年使用:0次
2023-07-11更新
|
498次组卷
|
7卷引用:陕西省汉中市2022-2023学年高二下学期期末文科数学试题
陕西省汉中市2022-2023学年高二下学期期末文科数学试题陕西省汉中市2022-2023学年高二下学期期末理科数学试题云南省楚雄州2022-2023学年高二下学期期末考试数学试题(已下线)第24讲 抛物线的简单几何性质6种常见考法归类(1)(已下线)第05讲 3.3.1抛物线及其标准方程(8类热点题型讲练)-【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)3.3 抛物线(精练)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)(已下线)专题13 抛物线的标准方程5种常见考法归类-【考点通关】2023-2024学年高二数学高频考点与解题策略(苏教版2019选择性必修第一册)
解题方法
9 . 设
为抛物线
的焦点,
是抛物线
的准线与
轴的交点,
是抛物线
上一点,当
轴时,
.
(1)求抛物线
的方程.
(2)
的延长线与
的交点为
,
的延长线与
的交点为
,点
在
与
之间.
(i)证明:
,
两点关于
轴对称.
(ii)记
的面积为
,
的面积为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3baa6d3cf25af55055fb8e1c4dcccd91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323232ab36943d1d5d2831d70ffcff87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a780261d7c91ccf6b5dc0f580146b1a4.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(i)证明:
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a0c85deb80d8e63bc60127e803f7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d4c08ed526b54460c4d6fda1c11b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d7df4d3cf520d9d9355394c0a884bb.png)
您最近一年使用:0次
2024-02-05更新
|
525次组卷
|
3卷引用:河北省邢台市2024届高三上学期期末数学试题
解题方法
10 . 探照灯、汽车灯等很多灯具的反光镜是抛物面(其纵断面是拋物线的一部分),正是利用了抛物线的光学性质:由其焦点射出的光线经抛物线反射之后沿对称轴方向射出.根据光路可逆图,在平面直角坐标系中,抛物线
,一条光线经过
,与
轴平行射到抛物线
上,经过两次反射后经过
射出,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd426e7e1e65d91394da0b28d49f65.png)
________ ,光线从点
到
经过的总路程为________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/853c5b83-fc2b-492e-873b-9c7170867603.png?resizew=100)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a11db9cfc93cd1134b388ff5fbeea0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0145ad62ecc8ae00569ef2bd4ac5ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd426e7e1e65d91394da0b28d49f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/853c5b83-fc2b-492e-873b-9c7170867603.png?resizew=100)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/c7f6d403-b1a2-4dc9-af2e-5c3ddc166f66.png?resizew=193)
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