1 . 已知平面内一动点
到点F(1,0)的距离与点
到
轴的距离的差等于1.
(1)求动点
的轨迹
的方程;
(2)过点
作两条斜率存在且互相垂直的直线
,设
与轨迹
相交于点
,
与轨迹
相交于点
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/44434b647ec546fe787e2164e0be6cd2.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/01c74a907dda6bb7d9d56d009d9df253.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/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbace01eb5d6f2a4649fbb6c1ae94ab5.png)
您最近一年使用:0次
2019-01-30更新
|
2057次组卷
|
10卷引用:2011年湖南省普通高等学校招生统一考试文科数学
2011年湖南省普通高等学校招生统一考试文科数学(已下线)2013届江西南昌10所省重点中学高三第二次模拟数学试卷(五)(已下线)2013届江西省吉安县二中高三4月月考数学文理合卷试卷(已下线)2014年高考数学全程总复习课时提升作业五十八第八章第九节练习卷(已下线)专题9.7 抛物线(练)【理】-《2020年高考一轮复习讲练测》福建省莆田第九中学2017-2018学年高二上学期第二次月考(12月)数学试题2018秋高中数学人教A版选修1-1第二章:圆锥曲线与方程 评估验收(二)沪教版(上海) 高二第二学期 新高考辅导与训练 第12章 圆锥曲线 本章复习题(已下线)【新东方】杭州新东方高中数学试卷326江苏省徐州市第七中学2022-2023学年高二上学期10月月考数学试题
名校
2 . 已知抛物线y2=2px(p>0)上点M(3,m)到焦点F的距离为4.
(Ⅰ)求抛物线方程;
(Ⅱ)点P为准线上任意一点,AB为抛物线上过焦点的任意一条弦,设直线PA,PB,PF的斜率为k1,k2,k3,问是否存在实数λ,使得k1+k2=λk3恒成立.若存在,请求出λ的值;若不存在,请说明理由.
(Ⅰ)求抛物线方程;
(Ⅱ)点P为准线上任意一点,AB为抛物线上过焦点的任意一条弦,设直线PA,PB,PF的斜率为k1,k2,k3,问是否存在实数λ,使得k1+k2=λk3恒成立.若存在,请求出λ的值;若不存在,请说明理由.
您最近一年使用:0次
2018-08-30更新
|
483次组卷
|
5卷引用:湖南省长沙市宁乡一中2018-2019学年高三上学期10月月考文科数学试题
名校
解题方法
3 . 设斜率不为0的直线
与抛物线
交于
两点,与椭圆
交于
两点,记直线
的斜率分别为
.
(1)求证:
的值与直线
的斜率的大小无关;
(2)设抛物线
的焦点为
,若
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91356fe1338cd458e4b1761b36873145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4e4c7a79d9d3cdb9ac5949d53e33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40747509ad1f8ea88a5c31ea20271081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422cbf74078aaee2e59fce1cbe25be27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d76cf4e4cd92d767bafc6c31ebaaf71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa0eefe088505066dc88d4b395e77cd.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4e20e5bb12a39f38f455893d5948d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
(2)设抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91356fe1338cd458e4b1761b36873145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca18ef35576fa331defd7ea388abb9a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fb2555e435086845a6d06e73e3c9ff.png)
您最近一年使用:0次
2018-04-27更新
|
665次组卷
|
2卷引用:【全国市级联考】湖南省永州市2018届高三下学期第三次模拟考试数学(理)试题
名校
解题方法
4 . 在平面直角坐标系中,动点
(
)到点
的距离与到
轴的距离之差为1.
(1)求点
的轨迹
的方程;
(2)若
,过点
作任意一条直线交曲线
于
,
两点,试证明
是一个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19934cfed158057bc208f942f898fe2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c699a757a7ee06c063150def9c5dffa.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/e7b0a9091b9f2f980536350127691fa7.png)
您最近一年使用:0次
2018-03-11更新
|
958次组卷
|
5卷引用:2018年湖南省高三十四校联考文科数学
2018年湖南省高三十四校联考文科数学(已下线)2018年高考数学备考中等生百日捷进提升系列(综合提升篇) 专题05 解析几何解答题(已下线)《高频考点解密》—解密23 曲线与方程(已下线)解密21 曲线与方程-备战2018年高考文科数学之高频考点解密重庆市南开中学校2021-2022学年高二上学期11月月考数学试题
解题方法
5 . 已知抛物线
的焦点
与椭圆Γ:
的一个焦点重合,点
在抛物线上,过焦点
的直线
交抛物线于
,
两点.
(1)求抛物线
的方程以及
的值;
(2)记抛物线
的准线与
轴交于点
,试问是否存在常数
,使得
且
都成立?若存在,求出实数
的值; 若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7585c7944d095b903c6e0d3dcbc228e.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/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8aed33984ccc91282d8a1c2be27cd0.png)
(2)记抛物线
![](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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd9736828195f010db4e1f0a9dea7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce97701a2f599401f400a604ae0c66d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47335c411abfddcfe3e7d64e94bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
6 . 已知抛物线
的焦点
与椭圆
的一个焦点重合,点
在抛物线上,过焦点
的直线
交抛物线于
、
两点.
(1)求抛物线
的标准方程以及
的值.
(2)记抛物线的准线
与
轴交于点
,试问是否存在常数
,使得
,且
都成立.若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29e9ff132637709ce7c3f58cfcd4da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7585c7944d095b903c6e0d3dcbc228e.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/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8aed33984ccc91282d8a1c2be27cd0.png)
(2)记抛物线的准线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce97701a2f599401f400a604ae0c66d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47335c411abfddcfe3e7d64e94bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2017-11-18更新
|
1169次组卷
|
3卷引用:湖南师大附中2018届高三上学期月考试卷(三)(11月) 数学文
解题方法
7 . 已知抛物线
,过动点
作抛物线的两条切线,切点分别为
,且
.
(1)求点
的轨迹方程;
(2)试问直线
是否恒过定点?若恒过定点,请求出定点坐标;若不恒过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2277a312efafbb543d0273541071f9a0.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)试问直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2017-05-14更新
|
859次组卷
|
2卷引用:湖南省衡阳市2017届高三下学期第三次联考数学(文)试题
名校
8 . 已知抛物线
的焦点为
,过点
作倾斜角为
的直线
与抛物线
在第一、四象限分别交于
两点,则
的值等于________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.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/2d5bca00fa20e6e80480b9d06d2e52ee.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d54cedbfc22f09a728b34ce129dbc46f.png)
您最近一年使用:0次
2016-12-04更新
|
2288次组卷
|
9卷引用:2016届湖南宁远县一中高三下学期模拟考试数学(理)试卷
解题方法
9 . 已知直线
的斜率为
,它与抛物线
相交于
两点,
为抛物线的焦点, 若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a9a49dc8499d6c3b73d633e20b9757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ab21cf4f8f8ffa5dafd65eeb72c99a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2016-12-04更新
|
911次组卷
|
3卷引用:2017届湖南师大附中高三上入学摸底文科数学试卷
10 . 过抛物线
的焦点F作斜率分别为
的两条不同的直线
,且
,
相交于点A,B,
相交于点C,D.以AB,CD为直径的圆M,圆N(M,N为圆心)的公共弦所在的直线记为
.
(I)若
,证明;
;
(II)若点M到直线
的距离的最小值为
,求抛物线E的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a69ab234c3a8a40a9d0a9620df498af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec7bcf5820dfe70290259c2d7ac1ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe42865a8ca3fe91e104273a4174e079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46fbee1091c01d2752d3ec2e804bf9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(I)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90931781b834d100def5e571c28486db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc119913022c0911844ab30307982a41.png)
(II)若点M到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97814cbb7a07b2e5726d144f97ebf444.png)
您最近一年使用:0次
2016-12-02更新
|
3129次组卷
|
3卷引用:2013年全国普通高等学校招生统一考试理科数学(湖南卷)