1 . 已知抛物线
的焦点为
,直线
交抛物线于
,
两点,以线段
为直径的圆交
轴于
,
两点,交准线
于
点,则下面结论正确的是:( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1dc3b2ca5b5e71f6f7acab671c8dc9.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.以![]() ![]() | B.![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
名校
解题方法
2 . 如图抛物线
的顶点为
,焦点为
,准线为
,焦准距为
;抛物线
的顶点为
,焦点也为
,准线为
,焦准距为
.
和
交于
、
两点,分别过
、
作直线与两准线垂直,垂足分别为
,过
的直线与封闭曲线
交于
、
两点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70f280d062923a39c0c881aad5d429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](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/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3113c748ec660388c3ae764f40a309f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70f280d062923a39c0c881aad5d429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3113c748ec660388c3ae764f40a309f.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b553e73d33069e54eb7fa0b62ce60421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
A.![]() | B.四边形![]() ![]() |
C.![]() | D.![]() ![]() |
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3卷引用:四川省雅安市天立教育集团2023-2024学年高二下学期开学考试数学试题
3 . 对每个正整数
是抛物线
上的点,过焦点
的直线
交抛物线于另一点
.
(1)证明:
;
(2)取
,并记
,求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45e6c5320f1615e1288057c79c0dcdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e808c00d132c5833c3875b6274908f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a3765f6f6b85240bc9b1a83697841a4.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0137c9fba1ab732a1d2f36a255a4fa9.png)
(2)取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116b0cb31f0d12ceaa50ec16af4aaf2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ceb7355215ca64b1ab5eb3d0c119054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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4 . 设拋物线
的焦点是
,直线
与抛物线
相交于
两点,且
,线段
的中点
到拋物线
的准线的距离为
,则
的最小值为( )
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8098a6b57a05154a5c154c03ed96ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211f11b5b5262dae696554a0145df6ce.png)
A.![]() | B.![]() | C.3 | D.![]() |
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|
1153次组卷
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8卷引用:四川省广安市第二中学校2022-2023学年高二上学期第三次月考数学(理)试题
四川省广安市第二中学校2022-2023学年高二上学期第三次月考数学(理)试题四川省泸县第五中学2022-2023学年高二下学期3月月考理科数学试题重庆市长寿中学校2022-2023学年高二上学期期末数学试题江苏省无锡市南菁高级中学2023-2024学年高二上学期期末模拟数学试题江苏省南通市如东县2023-2024学年高二上学期期末学情检测数学试卷云南省曲靖市第二中学学联体2023届高三上学期第一次联考数学试题(已下线)江苏省七市2022届高三下学期第二次调研考试数学试题变式题6-10(已下线)模块八 专题7 以解析几何为背景的压轴小题
名校
解题方法
5 . 已知抛物线C:
,F为抛物线C的焦点,
是抛物线C上点,且
;
(1)求抛物线C的方程;
(2)过平面上一动点
作抛物线C的两条切线PA,PB(其中A,B为切点),求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2040b8fae7f5af94b0d911ab6255da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532bcbe8307e6b2129bdcdbd553ee5f3.png)
(1)求抛物线C的方程;
(2)过平面上一动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864a1045399e9970fe9684e9644dc061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e5109b55b3b96af00c792527c77cca.png)
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|
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8卷引用:湖北省荆州中学2022-2023学年高二上学期期末数学试题
湖北省荆州中学2022-2023学年高二上学期期末数学试题(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)2023-2024学年高二上学期期末数学仿真模拟试题02(新高考地区专用)2023-2024学年高二上学期期末仿真模拟数学试题05(新高考地区专用)江西省(东乡一中、都昌一中、丰城中学、赣州中学、景德镇二中、上饶中学、上栗中学、新建二中)新八校2022届高三下学期第二次联考数学(文)试题(已下线)2022年全国高考甲卷数学(文)试题变式题13-16题(已下线)2022年全国高考甲卷数学(文)试题变式题21-23题(已下线)模块八 专题9 以解析几何为背景的压轴解答题
6 . 在平面直角坐标系
中,一动圆经过点
且与直线
相切,设该动圆圆心的轨迹为曲线K,P是曲线K上一点.
(1)求曲线K的方程;
(2)过点A且斜率为k的直线l与曲线K交于B、C两点,若
且直线OP与直线
交于Q点.求
的值;
(3)若点D、E在y轴上,
的内切圆的方程为
,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
(1)求曲线K的方程;
(2)过点A且斜率为k的直线l与曲线K交于B、C两点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554a2df2f0d3a975fd99b4cce411b7ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca65af952215ed07b6a5686dc4381d3a.png)
(3)若点D、E在y轴上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550d183b05000722c74baf25eb4a6741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
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7 . 过抛物线
的焦点
作直线交抛物线于
,
两点,
为线段
的中点,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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.以线段![]() ![]() |
B.以线段![]() ![]() |
C.当![]() ![]() |
D.![]() ![]() |
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2022-03-25更新
|
969次组卷
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5卷引用:重庆市主城区六校2021-2022学年高二上学期期末联考数学试题
名校
解题方法
8 . 设抛物线
:
的焦点为
,抛物线
上一点
的横坐标为
,过点
作抛物线
的切线
,与
轴交于点
,与
轴交于点
,与直线
:
交于点
.当
时,
.
(1)证明:
为等腰三角形,并求抛物线
的方程;
(2)若
为
轴左侧抛物线
上一点,过
作抛物线
的切线
,与直线
交于点
,与直线
交于点
,求
面积的最小值,并求取到最小值时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/d59d0981710daa289c46a23d34435517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fae1e77288490ead83a82e7eb8360b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4cad9613154e7c15f0fe0f607ebfb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f0533597752a0efee17b335e548a72.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2698f08d94afa1cd5b81444791f4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/c5db41a1f31d6baee7c69990811edb9f.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
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2022-03-23更新
|
262次组卷
|
2卷引用:重庆市西南大学附属中学校2021-2022学年高二(广延班)下学期第三次月考数学试题
名校
解题方法
9 . 已知抛物线
的焦点
到其准线的距离为4,圆
,过
的直线
与抛物线
和圆
从上到下依次交于
四点,则
的最小值为_________ .
![](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/42103f88b80e7ef8bb12c7b839990a5f.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf810c8f387bbc753030c14e069d8d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b30fadc6a4933dc7588398687e3c8f4.png)
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2021-06-03更新
|
1148次组卷
|
6卷引用:河南省豫北名校2021-2022学年高二下学期5月调研考试理科数学试题
河南省豫北名校2021-2022学年高二下学期5月调研考试理科数学试题江苏省扬州市新华中学2022-2023学年高二上学期期中数学试题江苏省盐城中学2021届高三下学期仿真模拟数学试题江苏省南京市第二十九中学2021-2022学年高三上学期期初第三次学情调研数学试题(已下线)广东省深圳市横岗高级中学2022届高三上学期9月第一次月考数学试题(已下线)专题25 圆锥曲线压轴小题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)
名校
解题方法
10 . 已知抛物线
的焦点为
,过点
的直线
交抛物线于
、
两点,以线段
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两点,设线段
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A.![]() |
B.若![]() ![]() ![]() |
C.若抛物线上存在一点![]() ![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() |
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2020-12-23更新
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6卷引用:专题13 《圆锥曲线与方程》中的存在性问题(2)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
(已下线)专题13 《圆锥曲线与方程》中的存在性问题(2)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) 江苏省南京市六校联合体2020-2021学年高三上学期12月联考数学试题河北省石家庄市第二中学2022届高三下学期3月月考数学试题河北省廊坊市第一中学2023届高三上学期11月月考数学试题吉林省延边州2023届高三统考二模数学试题(已下线)专题09 平面解析几何