名校
1 . 已知双曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a259dddccc3cfe8f81735cd5834785d.png)
的左、右焦点分别为
,其中
也是抛物线
的焦点,
与
在一象限的公共点为
,若直线
斜率为
,则双曲线离心率
为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a259dddccc3cfe8f81735cd5834785d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5d22b84e0337fffed59bcf2e3115a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c9c87eba774f6bc072663d32d11fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/122c7e0a400e7114f31a01efc4e2a00f.png)
您最近一年使用:0次
2018-12-24更新
|
1455次组卷
|
6卷引用:广东省惠州市2019-2020学年高三第三次调研考试理科数学试题
广东省惠州市2019-2020学年高三第三次调研考试理科数学试题重庆市沙坪坝区南开中学2018-2019学年高二上学期期中考试数学(理)试题山东省淄博市淄博实验中学2019-2020学年高二上学期12月月考数学试题(已下线)技巧02 填空题解法与技巧 第二篇 解题技巧篇(练)-2021年高考数学二轮复习讲练测(浙江专用)(已下线)专题9-1 圆锥小题压轴九类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)江西省宜春市奉新县第一中学2021-2022学年高二下学期第一次月考数学(理)试题
名校
解题方法
2 . 设
是抛物线
的焦点,直线
与抛物线
交于
、
两点,
为坐标原点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4300cdebb4dee5a135c5ed2b706b9cd.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/1dde8112e8eb968fd042418dd632759e.png)
A.![]() |
B.![]() ![]() |
C.若![]() ![]() |
D.若在抛物线上存在唯一一点![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2021-07-30更新
|
667次组卷
|
4卷引用:广东省广州深圳四校(广雅、华附、省实、深中)2020-2021学年高二下学期期末联考数学试题
广东省广州深圳四校(广雅、华附、省实、深中)2020-2021学年高二下学期期末联考数学试题广东省深中、华附、广雅、省实2023-2024学年高二下学期期末联考模拟数学试卷(已下线)第十一章 圆锥曲线专练18—抛物线综合练习2-2022届高三数学一轮复习黑龙江省哈尔滨师范大学附属中学2021-2022学年高二下学期开学摸底考试数学试题
解题方法
3 . 抛物线有这样一个重要性质:从焦点发出的光线经过抛物线上一点(不同于抛物线的顶点)反射后,反射光线平行于抛物线的对称轴.若抛物线
(
)的焦点为F,从点F发出的光线经过抛物线上点M反射后,其反射光线过点
,且
,则△FMN的面积为( )
![](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/fc22a98b483745ec27139b431b3e2aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684cc74870c6dbbc2d48eff82e31075a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
4 . 设抛物线
(
)的焦点为
,准线为
,过抛物线上一点
作
的垂线,垂足为
,设
,
与
相交于点
,若
,且
的面积为
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dea65a23bc74cbbd93ddb21cb2f2c65.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/0f85fca60a11e1af2bf50138d0e3fe62.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78214cc6bb930184dbed5a53f153b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.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/51245131c14004c7e54c456817cd8d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33c2aa4cb5a3b8da3b188ab6a21520c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af2fdf1944afebb51cb6a5e6c74aadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2016-12-04更新
|
1445次组卷
|
12卷引用:【全国百强校】广东省佛山市第一中学2018-2019学年高二下学期第一次月考数学(文)试题
【全国百强校】广东省佛山市第一中学2018-2019学年高二下学期第一次月考数学(文)试题2016年全国普通高等学校招生统一考试理科数学(天津卷精编版)天津市第一中学2017届高三下学期第五次月考数学(理)试题安徽省定远重点中学2017-2018学年高二上学期期末考试数学(理)试题【全国市级联考】广西壮族自治区岑溪市2017-2018学年高二下学期期末考试数学(文)试题2018年春高考数学(理)二轮专题复习训练:专题四 解析几何、坐标系与参数方程山西省长治市第二中学2018-2019高二下学期期中考试数学(文)试卷2020届湖北省武汉中学高三下学期第二次教学质量检测理科数学试题(已下线)专题05 平面解析几何-五年(2016-2020)高考数学(理)真题分项(已下线)2016年全国普通高等学校招生统一考试理科数学(天津卷参考版)(已下线)专题17 解析几何多选、填空(理科)-2专题10平面解析几何(第二部分)
名校
5 . 已知动点
到定直线
:
的距离比到定点
的距离大2.
(1)求动点
的轨迹
的方程;
(2)在
轴正半轴上,是否存在某个确定的点
,过该点的动直线
与曲线
交于
,
两点,使得
为定值.如果存在,求出点
坐标;如果不存在,请说明理由.
![](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/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63309dbc3612815f6dbdee23d9a10adc.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd30b90e26ed653ee73be6b144321b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2018-06-05更新
|
1508次组卷
|
4卷引用:广东省揭阳市惠来县第一中学2021-2022学年高二上学期第二次阶段考试数学试题
名校
6 . 已知平面上动点
到点
距离比它到直线
距离少1.
(1)求动点
的轨迹方程;
(2)记动点
的轨迹为曲线
,过点
作直线
与曲线
交于
两点,点
,延长
,
,与曲线
交于
,
两点,若直线
,
的斜率分别为
,
,试探究
是否为定值?若为定值,请求出定值,若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a08e1f3a9fc4265c20cb381071a322e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)记动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a08e1f3a9fc4265c20cb381071a322e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65368687df4d7e3b9304e85ec4de354c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/67351fe10fcfc3f9072eec4c60bfaaa5.png)
您最近一年使用:0次
2019-05-06更新
|
857次组卷
|
2卷引用:广东省深圳市南山区华侨城中学2020届高三下学期线上测试(一)理科数学试题
名校
解题方法
7 . 已知抛物线
的焦点为
,其准线与
轴交于点
,过
作直线
与抛物线交于
、
两点,则
的取值范围为______________ .
![](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/5963abe8f421bd99a2aaa94831a951e9.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c49920ee46f7e1011b9b7cb7e12dcb.png)
您最近一年使用:0次
2019-06-06更新
|
783次组卷
|
2卷引用:广东省广州科学城中学2023届高三下学期5月月考数学试题
8 . 在平面直角坐标系中,曲线
:
和函数
的图像关于点
对称.
(1)函数
的图像和直线
交于
、
两点,
是坐标原点,求证:
;
(2)求曲线
的方程;
(3)对于(2),依据课本章节《圆锥曲线》的抛物线的定义,求证:曲线
为抛物线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2329774440278b274651ca465704a856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a696e905221dce884831403801cb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a696e905221dce884831403801cb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa657237b62ba1ce4b2064e5f018fea.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac51bffb8f476896081027b33f7ec25d.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(3)对于(2),依据课本章节《圆锥曲线》的抛物线的定义,求证:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
您最近一年使用:0次
2020-10-23更新
|
467次组卷
|
2卷引用:广东省深圳市宝安区2020-2021学年高二上学期期末数学试题
名校
9 . 已知抛物线
的焦点为
,准线
,点
在抛物线
上,点
在准线
上,若
,且直线
的斜率
,则
的面积为__________ .
![](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/40576c66720163494c3d71906a206a2c.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7a0b55fa88dabda8d0898bc4c5a434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e1712703e2832bebae13b1b7fc82ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2faf3bebb0ba48c18fed0cab7f045a78.png)
您最近一年使用:0次
2018-02-10更新
|
727次组卷
|
6卷引用:广东广雅中学2022-2023学年高二上学期12月月考数学试题
名校
10 . 已知抛物线
的焦点为F,F关于原点的对称点为P,过F作
轴的垂线交抛物线于M,N两点,给出下列三个结论:
①
必为直角三角形;
②直线
必与抛物线相切;
③
的面积为
.其中正确的结论是___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec1f8a14b2c1570aa076166017ccf33.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec1f8a14b2c1570aa076166017ccf33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223ec16c7b0b7d25431d352d89215462.png)
您最近一年使用:0次
2019-02-02更新
|
444次组卷
|
2卷引用:【市级联考】广东省惠州市2018-2019学年高二第一学期期末考试数学(理科)试题