1 . 已知点
在抛物线
的准线上,过点
作直线
与抛物线
交于
两点,斜率为2的直线与抛物线交于
两点.
(1)求抛物线
的标准方程;
(2)① 求证:直线
过定点
;
② 若
的面积为
,且满足
,求直线
斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc2de9df8bce6139613bb86322db0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.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/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e478787ebfeb68a5a7594dbd9eecd4.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)① 求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
② 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c8bef41fa6778e5eb57e2f19ea48f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-01-27更新
|
262次组卷
|
3卷引用:湖北省武汉外国语学校2023-2024学年高二上学期期末考试数学试题
湖北省武汉外国语学校2023-2024学年高二上学期期末考试数学试题江苏省徐州市沛县第二中学2024届高三下学期期初测试数学试题(已下线)2.4.2 抛物线的性质(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
2 .
表示以点
为中心的椭圆,如图所示,
为椭圆C:
的左焦点,Q为直线
上的一点,P为椭圆C上的一点,以
为边作正方形
(F,P,A,B按逆时针排列),当P在椭圆上运动时,
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5d275721db46e39e5b23a7f2b64268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9799b1b1f49ef15916b0018547564590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa04eb7cae40ce5e89da590b9cdb75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134dde7006742eba3252cb11fe959abe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f739b07f992bce672aef2fc48b4b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c2293f93791a597bf0162411f3395f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857e804aac2f81757178d237485299fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65ea04098e8d2809d8163f27d49860c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/cf3db5f3-5935-4e04-8948-1081f9a525e9.png?resizew=187)
您最近一年使用:0次
3 . 如图,一隧道内设双行线公路,其截面由一个长方形和抛物线构成.为保证安全,要求行驶车辆顶部(设为平顶)与隧道顶部在竖直方向上高度之差不小于
,已行车道AB总宽度
,则车辆通过隧道的限制高度为__________ m.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d77ecfc44c94b32a7fcc565e2ebbe4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e10630bd256876b0a3ba90c879203b8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/a5efaa66-e652-43c4-89d3-43148e2696dd.png?resizew=169)
您最近一年使用:0次
名校
4 . 已知首项为
,公比为q的等比数列
,其前n项和为
,则“
”是“
单调递增”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b67857a043caf87b55d38401d0d9062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.充分不必要条件 | B.必要不充分条件 | C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2024-01-26更新
|
853次组卷
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3卷引用:北京市通州区2023-2024学年高二上学期期末质量检测数学试卷
名校
5 . 如图,椭圆
与双曲线
有公共焦点
,椭圆的离心率为
,双曲线的离心率为
,点
为两曲线的一个公共点,且
为
的内心,
三点共线,且
轴上点
满足
,则
的最小值为__________ ;
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29eb5ce3f09c49dfa489a3b0bd5beafb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65abb60103949a9cbe1e4890df8bd3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8597c617617900e3265b9eacb0fed1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eadd9ffa5f17a464c7b1eba82f68f386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78385e289193ff6bea96956b1126295e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7da98a8220a45b0cc4a665ebac80ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120f812ad42739155a1337e7d5a7bcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c07b101a1a118c7558a9e59b13c95c.png)
您最近一年使用:0次
6 . 椭圆
的焦点坐标为 ______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c190e8bb81a4d26cf638ed246193cc9.png)
您最近一年使用:0次
解题方法
7 . 2022年4月16日9时56分,神舟十三号返回舱成功着陆,返回舱是宇航员返回地球的座舱,返回舱的轴截面可近似看作是由半圆和半椭圆组成的“曲圆”.如图,在平面直角坐标系中半圆的圆心在坐标原点,半圆所在的圆过椭圆的焦点
,椭圆的短轴与半圆的直径重合,下半圆与
轴交于点
.若过原点
的直线与上半椭圆交于点
,与下半圆交于点
,则下列说法正确的个数有:( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/24e511fb-849d-4505-bd70-679d3a9596cb.jpg?resizew=354)
①椭圆的长轴长为4
②线段
长度的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8529293cdece88162a8f5bace67151b7.png)
③
面积的最小值是3
④
的周长为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1734bef717187708351c1be3bd035071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9654b0a972511f2b28a292c1d4a1e770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/24e511fb-849d-4505-bd70-679d3a9596cb.jpg?resizew=354)
①椭圆的长轴长为4
②线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8529293cdece88162a8f5bace67151b7.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7572ecc467c061ef71cf4486ec63ec3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1734bef717187708351c1be3bd035071.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
解题方法
8 . 已知双曲线
的左、右顶点分别为
,离心率为
.过点
的直线l与C的右支交于M,N两点,设直线
的斜率分别为
.
(1)若
,求
;
(2)证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9c11cc36320090d0aaf0c621a63b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8f7e40ba386c0a9675896b52752d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e4cfa2db814e7e2e8abdf033706420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e607c2f7ae494246768832acb0d54a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3342ecc389773431bc3f64410e41191.png)
您最近一年使用:0次
解题方法
9 . 已知
为椭圆
的右焦点,
是椭圆上一动点,点
为圆
上一动点,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.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/deab0fbe4cc4538c7655e5f7a6f817eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44397211d1486df32b56d8d213695170.png)
您最近一年使用:0次
解题方法
10 . 已知过双曲线
左焦点
且倾斜角为60°的直线与C交于点A,与y轴交于点B,且A是
的中点,则C的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c8091d78595c42d437ff5766431a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
您最近一年使用:0次
2024-01-25更新
|
395次组卷
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3卷引用:河南省开封市2023-2024学年高二上学期期末调研考试数学试卷
河南省开封市2023-2024学年高二上学期期末调研考试数学试卷(已下线)2.3.2 双曲线的性质(二十二大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)河南省开封市2024届高三下学期第二次质量检测数学试题