2024高三下·全国·专题练习
1 . 关于曲线
有以下五个结论:
①当
时,曲线C表示圆心为
,半径为
的圆;
②当
,
时,过点
向曲线C作切线,切点为A,B,则直线AB的方程为
;
③当
,
时,过点
向曲线C作切线,则切线方程为
;
④当
时,曲线C表示圆心在直线
上的圆系,且这些圆的公切线方程为
或
;
⑤当
,
时,直线
与曲线C表示的圆相离.
以上正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983416abb2a19329feee784025961f1a.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484121f8076509e579f91dd919e4632a.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4681073487d89441a8db549f4187dda8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e729c58c343ef3cebb8bd720278c26ed.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d694b4de9f0bef15f2917a4ed214e01c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9891da64b7a4a2f83f2af4d4c313246e.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e8c8fd6d9c4ed8cf35504db1918b4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a10732055a4228ab2b1a0f1bb16b67.png)
⑤当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1578a4b2d61c2b65532f5dcb25003.png)
以上正确结论的序号为
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2 . 已知点
,定义
为
的“镜像距离”.若点
在曲线
上,且
的最小值为2,则实数
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07dcd9bfd79cb83eef32ffecb3660d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5aded785faf38e963d402f622be4092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ebfda261c4a27e1fa2ee5fc6d4bdfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 一只蜜蜂从蜂房
出发向右爬,每次只能爬向右侧相邻的两个蜂房 (如图),例如:从蜂房
只能爬到
号或
号蜂房,从
号蜂房只能爬到
号或
号蜂房……以此类推,用
表示蜜蜂爬到
号蜂房的方法数,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e8b81416d0ab26616288b2c5e8333a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 将“用一条线段联结两个点”称为一次操作,把操作得到的线段称为“边”.若单位圆上
个颜色不相同且位置固定的点经过
次操作后,从任意一点出发,沿着边可以到达其他任意点,就称这n个点和k条边所构成的图形满足“条件
”,并将所有满足“条件
”的图形个数记为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33489e1a3bd3857a818bb0c6296da53a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b68080f1b8f75112406c0c5a8a0a93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33489e1a3bd3857a818bb0c6296da53a.png)
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7卷引用:6.2.3组合-6.2.4组合数——课时作业(提升版)
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5 .
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)
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6 . 中国传统数学中开方运算暗含着迭代法,清代数学家夏鸾翔在其著作《少广缒凿》中用迭代法给出一个“开平方捷术”,用符号表示为:已知正实数
,取一正数
作为
的第一个近似值,定义
,则
是
的一列近似值.当
时,给出下列四个结论:①
;②
;③
,
;④
,
.其中所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55dde645fdd5795b4194e50d6885bf17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e40ebe5a203db35552e27bf3f079f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da18ad56af5e38b1a5b73f44ba198fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55dde645fdd5795b4194e50d6885bf17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede0f7cac4530e0ed4799a8192283888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835faec9f80596430d7352dcacde9589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c3401c74f3b70fd95a069b6abcf717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3febfa17c874de45558534cc8bbe8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e377f675489078f2fec21a6b5cce0c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c68b253787b7980d259a243ee42ecfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad46a14425d9c75b82b4e1342c57949e.png)
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解题方法
7 . 已知四边形
是椭圆
的内接四边形,其对角线
和
交于原点
,且斜率之积为
.给出下列四个结论:
①四边形
是平行四边形;
②存在四边形
是菱形;
③存在四边形
使得
;
④存在四边形
使得
.
其中所有正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caeb11677994ba487096958b1ad82ea1.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
①四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
②存在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
③存在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e84f14a77c27b015b6b1cf0896228b1.png)
④存在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d8d582c0bf83314b19df67e1bd2740.png)
其中所有正确结论的序号为
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2024-01-17更新
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3卷引用:2.2.2 椭圆的性质(十八大题型)(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)
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8 . 过点
作圆
(
为参数,且
)的两条切线分别切圆
于点
,
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4d8171374a7134e3d25b91fc4b198a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.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/395ae88d64693e119da73abe23109bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d08f0ab6e573253450e03427e13db1.png)
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9 . 定义:如果曲线段
可以一笔画出,那么称曲线段
为单轨道曲线 ,比如圆、椭圆都是单轨道曲线;如果曲线段
由两条单轨道曲线构成,那么称曲线段
为双轨道曲线 .对于曲线
有如下命题:
存在常数
,使得曲线
为单轨道曲线;
存在常数
,使得曲线
为双轨道曲线.下列判断正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14884a97cc2e3321b7fb6f6de2f31fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2023-12-13更新
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598次组卷
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9卷引用:2.5 曲线与方程(五大题型)(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)
(已下线)2.5 曲线与方程(五大题型)(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)上海市青浦区2024届高三上学期期终学业质量调研数学试题上海市吴淞中学2023-2024学年高二上学期期末质量检测数学试卷上海市同济大学第一附属中学2023-2024学年高二上学期期末考试数学试卷(已下线)第1章 坐标平面上的直线 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)第2章 圆锥曲线(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)专题07 解析几何(三大类型题综合)15区新题速递(已下线)专题01 集合(15区真题速递)(已下线)专题03 圆 曲线与方程(九大题型+优选提升题)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)
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解题方法
10 . 在平面直角坐标系
中, 已知两定点
, 点
满足
且在焦点在
轴正半轴的抛物线
上. 过
作一斜率存在的直线交
于
两点, 连接
交抛物线
于点
.
(1)求抛物线
的标准方程;
(2)判断直线
是否恒过定点,若是请求出该定点坐标,若不是请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485be495bd20b3a3f4653cb548b9a008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce26f799b5f11e73a50860e534f7ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91841d805c7c1f090148cae4c406f73c.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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