名校
解题方法
1 . 已知抛物线
的焦点为
,直线
均过点
分别交抛物线
于
四点,若直线
斜率乘积的绝对值为8,则当直线
的斜率为___________ 时,
的值最小,最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f63a76a5f78eb64e64b5a2c9f1553cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45d4785a48c4e9641450e9ee2822df3.png)
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2024-02-03更新
|
47次组卷
|
2卷引用:陕西省宝鸡市长岭中学2023-2024学年高二上学期期中考试数学试题
名校
解题方法
2 . 已知抛物线
的焦点
,过点
的直线
与抛物线交于
、
两点
,
,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/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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c663466d641b5fdfef1e529d6c330ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166afeb61d5a80366a8ae29c912cd644.png)
A.![]() | B.![]() |
C.![]() | D.以![]() ![]() |
您最近一年使用:0次
名校
3 . 平面内一点P满足:P点到
的距离比P点到y轴的距离大2,且点P不在y轴左侧,记点P的轨迹为曲线C.
(1)求曲线C的方程;
(2)点Q为y轴左侧一点,曲线C上存在两点A,B,使得线段点QA,点QB的中点均在曲线C上,设线段AB的中点为M,证明:
垂直于y轴.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae045f9b7daebb9f15b8769575f62484.png)
(1)求曲线C的方程;
(2)点Q为y轴左侧一点,曲线C上存在两点A,B,使得线段点QA,点QB的中点均在曲线C上,设线段AB的中点为M,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
您最近一年使用:0次
名校
解题方法
4 . 已知抛物线
:
,
:
,若直线l:
与
交于点A,B,且与
交于点P,Q,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed5cf0b4c918b2795034e5b2b53cd1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.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/2b9aa21530d864bd86e80d1a652b04a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
A.1 | B.2 | C.4 | D.6 |
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2024-01-04更新
|
462次组卷
|
3卷引用:陕西省榆林市十校2024届高三上学期12月联考数学(文)试题
名校
解题方法
5 . 已知抛物线
,垂直于
轴的直线
与圆
相切,且与
交于不同的两点
.
(1)求p;
(2)已知
,过
的直线与抛物线
交于
两点,过
作直线
的垂线,与直线
分别交于
两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7f565360cb8de963874291c7013118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e0c0b5bda80a9aa5b49b03ce2f9352.png)
(1)求p;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a42451bdbef6c82dbaf8e06f0614794.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a225b6550530973e4859ea29765c728a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a225b6550530973e4859ea29765c728a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a36d2f86d8560ef6a67a34cecb81494b.png)
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2023-12-29更新
|
286次组卷
|
3卷引用:陕西省名校协作体2024届高三上学期一轮复习联考(四)数学(文)试题
名校
解题方法
6 . 经过抛物线
的焦点
的直线
交
于
两点,
为坐标原点,设
,
的最小值是4,则下列说法正确的是()
![](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/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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75dba73fdfb9451fbe2b983682f1d8f1.png)
A.![]() |
B.![]() |
C.若点![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-12-27更新
|
994次组卷
|
7卷引用:陕西省榆林市五校联考2023-2024学年高二上学期12月月考数学试题
陕西省榆林市五校联考2023-2024学年高二上学期12月月考数学试题(已下线)模块五 专题1 期末全真模拟(基础卷1)高二期末河南省九师联盟洛阳强基联盟2023-2024学年高二上学期12月联考数学试题(已下线)期末精确押题之多选题(40题)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)重庆市部分学校2023-2024学年高二上学期1月阶段测试数学试题山东省东营市2023-2024学年高二上学期1月期末质量监测数学试题江西省景德镇市乐平中学2023-2024学年高二上学期期末数学试题
解题方法
7 . 已知直线
与圆
相切,交曲线
于点
,若
是坐标原点,则以
为圆心,以
为半径的圆与圆
的位置关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d499a21e40eecada13c79efd20245b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51666c1fe2e52b8fa3f94131595dd716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.相交 | B.内含 | C.外离 | D.外切 |
您最近一年使用:0次
2023-12-25更新
|
752次组卷
|
3卷引用:陕西省榆林市米脂中学2024届高三上学期第六次模拟考试数学(文)试题
名校
解题方法
8 . 已知抛物线
的焦点为
,过
且倾斜角为
的直线
交抛物线于
,
两点( )
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.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)
A.直线![]() ![]() | B.原点到直线![]() ![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
9 . 已知抛物线
,过点
的直线
与抛物线
交于
两点,若
,则直线
的斜率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64447af8454c613a58b11d9274d3da2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18e9b80fdeaa8bd3cf97b3c214448f2.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49a1538831e007a0e47ec5e1069bff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-24更新
|
421次组卷
|
5卷引用:陕西省商洛市2024届高三一模数学(文)试题
名校
10 . 已知抛物线
的焦点
在直线
上,直线
与抛物线交于点
(
为坐标原点),则下列说法中正确的是( )
![](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/a67ec5e2d1bf78be60da3165c34d337c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() | B.准线方程为![]() |
C.以线段![]() ![]() | D.直线![]() |
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