名校
1 . 已知
为抛物线
上的三个点,且
,当点
与原点О重合时,
,则下列说法中,正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a68919c5cf3775eb79dfc3fcfc2e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860b76e47ec09b73eee198cc86b33b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/890c3adc2db9d97a4353a5abaccd6519.png)
A.抛物线方程为![]() |
B.直线AB的倾斜角必为锐角 |
C.若线段AC的中点纵坐标为![]() ![]() |
D.当AB的斜率为2时,B点的纵坐标为![]() |
您最近一年使用:0次
名校
2 . 已知抛物线
和
所围成的封闭曲线
如图所示,点
在曲线
上,给定点
,则下列说法中不正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/940b4bdb-fad3-486f-bc90-fbe59e6f8f3c.png?resizew=162)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7d334f7186c612a2bac12ae5e0365e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6991563453cd366d99513c393d1ccd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/940b4bdb-fad3-486f-bc90-fbe59e6f8f3c.png?resizew=162)
A.任意![]() ![]() ![]() |
B.任意![]() ![]() ![]() |
C.存在![]() ![]() ![]() |
D.任意![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
3 . 已知椭圆的左、右焦点分别为
,
,抛物线
,且椭圆
与抛物线
相交于
两点,若
,则椭圆
的离心率的取值范围是( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
4 . 设抛物线C的焦点为F,点E是C的准线与C的对称轴的交点,点P在C上,若,则
( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
5 . 已知抛物线
:
与抛物线
:
,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/e42102c1c07562853219ca5918803a27.png)
A.过![]() ![]() ![]() | B.![]() ![]() |
C.与x轴平行的直线与![]() ![]() | D.不存在直线与![]() ![]() |
您最近一年使用:0次
2024-02-03更新
|
876次组卷
|
3卷引用:四川省成都市玉林中学2023-2024学年高二下学期3月诊断性评价数学试题
四川省成都市玉林中学2023-2024学年高二下学期3月诊断性评价数学试题安徽省合肥市第一中学2024届高三上学期期末质量检测数学试题(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)
名校
解题方法
6 . 已知边长为
的等边三角形的一个顶点位于原点O,另外两个顶点A,B在抛物线
上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6093eebca8f3ff82ce9298feb197e955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
7 . 如图,某种地砖ABCD的图案由一个正方形和4条抛物线构成,体现了数学的对称美.
,
,
,
,
,已知正方形ABCD的面积为64,连接
,
的焦点
,
,线段
分别交
,
于点G,H,则
的值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/fabd7244-7391-4d7f-994f-30486346a3c1.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c156c3b344e637b4f86404f2711940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1298e166d0529882c437d9a00a5cca37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e8fb323f9ebcb53496ece881183740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1272085b2880ed11a129063043ac07c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.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/b32c638e2bdff5fea14b34cc4f3c2eef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/fabd7244-7391-4d7f-994f-30486346a3c1.png?resizew=163)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
8 . 已知抛物线
的焦点为
,
是
上一点,且
到
的距离与
到
的对称轴的距离之差为2,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba52fa5306c0c5561f27fd4581c895f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/df5be1440d099f464ef46dee39de6010.png)
A.![]() | B.1 | C.2或4 | D.4或36 |
您最近一年使用:0次
2023-12-19更新
|
362次组卷
|
7卷引用:山东省多校2023-2024学年高二上学期12月联合质量检测数学试题
山东省多校2023-2024学年高二上学期12月联合质量检测数学试题河北省保定市部分高中2024届高三上学期12月联考数学试题山东省多校2023-2024学年高二上学期12月联合质量检测数学试题山东省省级联考2023-2024学年高二上学期12月月考数学试题(已下线)专题20 抛物线的定义和焦半径公式及抛物线的标准方程(期末选择题20)2023-2024学年高二数学上学期期末题型秒杀技巧及专项练习(人教A版2019)(已下线)3.3.2 抛物线的简单几何性质【第三练】“上好三节课,做好三套题“高中数学素养晋级之路(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)
23-24高二上·四川成都·阶段练习
名校
解题方法
9 . 已知椭圆:
:
的左、右焦点分别为
、
,右顶点为A,点M为椭圆
上一点,点I是
的内心,延长MI交线段
于N,抛物线
(其中c为椭圆下的半焦距)与椭圆
交于B,C两点,若四边形
是菱形,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658504df55afb5242d028af40c29fbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42fc33bcfc63ec2f4940ccd3f862400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7470ed4b6bbae29d3281a8a20a82dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a66a126a515b5e4d3fdc0bfeb7ba2c9.png)
A.![]() | B.椭圆![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
名校
解题方法
10 . 已知抛物线
:
经过
,
,
,
中的2个点,且焦点为
,
中的一个点.
(1)求
的方程;
(2)判断是否存在定直线
,过直线
上任意一点P作
的两条切线,切点分别为M,N,恒有
且直线
过
的焦点?若存在,求出
的方程,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04a0413aff67b2bd78c061408d5f45f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050ddc337e0c0855f5498c96b1717a62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a52e33aa409074fa1ef98bca650fe81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446c8abb735c4a157e70354406e382a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a534bc0f162800b2fbfe1cb844ad00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b54aa7512c326ce9d4ca6658b4f0b2ff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)判断是否存在定直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/9d3835e6398d18d162afebc92cd2ae9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次