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![]() |
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名校
2 . 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![]() ![]() |
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2024-02-03更新
|
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3卷引用: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
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)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
名校
解题方法
3 . 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)
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4 . 抛物线
的焦点为F.点F关于原点O的对称点为A.若以F为圆心的圆经过点A且与W的两个交点为B,C,则下面结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fba8cc28e9e1838394beda2393c1b87.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
5 . 已知点A是抛物线
上的动点,
为坐标原点,
为焦点,
,且
三点顺时针排列,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74de352eb2053f850f8367d54280be46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f5e21d225bf3c159ddf3876fbb8fb1.png)
A.当点![]() ![]() ![]() |
B.当点![]() ![]() ![]() |
C.当点A与点![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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名校
解题方法
6 . 如图拋物线
的顶点为
,焦点为
,准线为
,焦准距为4;抛物线
的顶点为
,焦点也为
,准线为
,焦准距为6.
和
交于
、
两点,分别过
、
作直线与两准线垂直,垂足分别为M、N、S、T,过
的直线与封闭曲线
交于
、
两点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/485d3071-49f1-4be3-b808-80f7e9aed40b.png?resizew=164)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.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/6aaafb050b24c4e806c480e0665aaa5a.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/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.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/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)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/485d3071-49f1-4be3-b808-80f7e9aed40b.png?resizew=164)
A.![]() | B.四边形![]() |
C.![]() | D.![]() ![]() |
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2023-04-19更新
|
2336次组卷
|
7卷引用:广东省佛山市2023届高三二模数学试题
广东省佛山市2023届高三二模数学试题(已下线)专题06 解析几何(已下线)押新高考第10题 解析几何综合专题18平面解析几何(多选题)(已下线)2023年新课标全国Ⅱ卷数学真题变式题6-10河北省衡水市安平中学2023-2024学年高二上学期第三次月考数学试题黑龙江省大庆铁人中学2023-2024学年高二上学期期末考试数学试题
7 . 已知抛物线
的焦点为
,圆
与
交于
两点,其中点
在第一象限,点
在直线
上运动,记
.
①当
时,有
;
②当
时,有
;
③
可能是等腰直角三角形;
其中命题中正确的有__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56648a303009f944e1a9983c3f62c7b6.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbc161cf1578e0c4971ec8fac62bbe2.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4990b135057293a0111b78fc068fa13b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50145f327f2e657a96b1c0362c88a012.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90680329d32003f001a232230afcfdeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d99ddb507b59edc658f634384a4c41.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
其中命题中正确的有
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2023-01-13更新
|
802次组卷
|
4卷引用:湖南省益阳市2022-2023学年高三上学期期末数学试题
解题方法
8 . 已知
为坐标原点,过圆
圆心的直线
交拋物线
于
两点、交圆
于
两点,
在
之间,当
时,
.则(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
___________ ;(2)
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320bb3b8ee3ff1466e6241042de12c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ed33bf7b3548361d3a7fea71b6cb57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050c88c50b513815867ae61049ba9725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd135d177ce12259bfa5aa67ee6d5a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01dea8283af83d2c9732e2ac6dc98acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449cac5b064090fca2531950fc8b2025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1faa8e626e59a36ab51af72c11153e.png)
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2022-01-23更新
|
584次组卷
|
5卷引用:山东省青岛市四区2021-2022学年高三上学期期末考试数学试题
山东省青岛市四区2021-2022学年高三上学期期末考试数学试题(已下线)专题五检测 解析几何-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)(已下线)思想02 分类与整合思想(练)--第三篇 思想方法篇-《2022年高考数学二轮复习讲练测(浙江专用)》(已下线)思想02 分类与整合思想(讲)--第三篇 思想方法篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》山东省青岛市4区县2021-2022学年高三上学期期末考试数学试题
名校
解题方法
9 . 如图,设
为
轴的正半轴上的任意一点,
为坐标原点.过点
作抛物线
的两条弦
和
,
、
在
轴的同侧.
![](https://img.xkw.com/dksih/QBM/2022/1/1/2885118365810688/2892413238779904/STEM/b7dcb6ff-7e7c-42be-b03a-77bff00d3619.png?resizew=227)
(1)若
为抛物线
的焦点,
,直线
的斜率为
,且直线
和
的倾斜角互补,求
的值;
(2)若直线
、
、
、
分别与
轴相交于点
、
、
、
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fbb6cbf601c8d08db363827baefc296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2022/1/1/2885118365810688/2892413238779904/STEM/b7dcb6ff-7e7c-42be-b03a-77bff00d3619.png?resizew=227)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800b8e0a7259c739368aab9c22c17d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab54c36aa318a5d987ed0fc9b520feff.png)
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21-22高二·江苏·单元测试
10 . 已知点
是抛物线M:
上的动点,
(1)点B是圆C:
上的动点,当
时,
,求抛物线方程;
(2)已知
,等边三角形
的三个顶点在抛物线M上,
的重心Q落在双曲线
上,求点Q坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f131565484188b69a1850a23d73b2068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
(1)点B是圆C:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a353d1a988596880c0a48c2303d20c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d318d706ca4ec954246a292293b91a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5bfa2f7ec46f818db87ea57568554b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faef8169baa38bb7af7212ea69fd99f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90201474e92440aea9a6e7277a8aa22c.png)
您最近一年使用:0次