23-24高二上·全国·课后作业
名校
解题方法
1 . 已知圆系
,圆
过
轴上的定点
,线段
是圆
在
轴上截得的弦,设
,
.对于下列命题:
①不论
取何实数,圆心
始终落在曲线
上;
②不论
取何实数,弦
的长为定值1;
③不论
取何实数,圆系
的所有圆都与直线
相切;
④式子
的取值范围是
.
其中真命题的序号是________ (把所有真命题的序号都填上)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44040d39dfe54c07501b97b31e35080a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66603dd2d326d41dd3da242c6373591b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd74a50518d45904e4295e95ece5ba3d.png)
①不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
②不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
③不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f3fa679bb55ded25a9b72a8e788cb1.png)
④式子
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c26ee0f01990cd336dc2452014ea0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49fac8ba3fd4c62ec08ed60a2fe44b2.png)
其中真命题的序号是
您最近一年使用:0次
2023·全国·模拟预测
解题方法
2 . 在平面直角坐标系
中,点
到点
的距离等于点
到直线
的距离,记动点
的轨迹为
.
(1)求
的方程;
(2)已知点
均在
上,且
,直线
与
的另一个交点分别为
,且
,求直线
的斜率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c41b2f7ca11db3aaea46c69286adbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a333645e37f429b295b8379f0e99dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8485a371c02563ce67b890cd302ae05a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ca520748c8b8d3878fb112a89ada7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79226929decdaeb124ee72a687ae6325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023·全国·模拟预测
解题方法
3 . 已知二元关系
,曲线
.
(1)若
,
,正方形ABCD的四个顶点在曲线
上,求正方形ABCD的面积;
(2)若
,设曲线
与x轴的交点为M,N,抛物线
与y轴的交点为G,直线MG与抛物线
交于点P,直线NG与抛物线
交于点Q,求证:直线PQ过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f212edfb5e742cbdb77729b89d6066f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bab860cd33d536a3a4d15ce0d6a86f8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f06408895febc126c2ae409e807349c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86304c3e26200299a0480641525a283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e784f813859bb081b36844b01a485409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
2023·全国·模拟预测
解题方法
4 . 已知点P,Q是圆
上的两个动点,若直线OP与OQ的斜率都存在且满足
.
(1)当
时,求PQ的中点M的轨迹方程;
(2)当
时,椭圆
与动直线PQ恒相切,求椭圆C的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1000c40056cb9ed50d7157b8dd998fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08be81d68cd0b6cd737f77f23e77be5e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4561e662151983a27b3e8c8fcc857f06.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6494bb8bce0f3656e612f38031b2c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
您最近一年使用:0次
名校
解题方法
5 . 如图所示,正方体
的棱长为3,动点
在底面正方形
内,且
与两个定点
,
的距离之比为
.
的轨迹方程,并说明轨迹的形状;
(2)求动点
到平面
的距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95628327dc58037e5368f4404c05ec39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8406f2441769ce49264ccca6585dc9.png)
您最近一年使用:0次
6 . 已知两定点
、
,动点P满足条件___,求动点P的轨迹方程.请从下列条件中任选一个补充到横线上,并在此条件下完成题目.
条件①:直线PM与直线PN垂直;
条件②:点P到M、N两点距离平方之和为20;
条件③:直线PM与直线PN斜率之积为4.
(注:如果选择的条件不符合要求,计0分;如果选择多个符合要求的条件分别作答,按第一个解答计分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6114ce586d4468f1b83c85bf029ba625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d7db32e5ff96b8bb59cac3851d3c4c.png)
条件①:直线PM与直线PN垂直;
条件②:点P到M、N两点距离平方之和为20;
条件③:直线PM与直线PN斜率之积为4.
(注:如果选择的条件不符合要求,计0分;如果选择多个符合要求的条件分别作答,按第一个解答计分)
您最近一年使用:0次
7 . 已知
、
,则下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
A.平面内满足![]() |
B.平面内满足![]() |
C.平面内满足![]() |
D.平面内满足![]() |
您最近一年使用:0次
2023-11-12更新
|
1607次组卷
|
12卷引用:浙江省台州山海协作体2023-2024学年高二上学期期中联考数学试题
浙江省台州山海协作体2023-2024学年高二上学期期中联考数学试题(已下线)第三篇 努力 “争取”考点 专题8 圆锥曲线的定义应用【练】海南省海口市农垦中学2023-2024学年高二上学期期中数学试题山西省大同市第一中学校2023-2024学年高二上学期12月月考数学试题山西省大同市第一中学校2023-2024学年高二上学期12月月考数学试题四川省凉山州宁南中学2023-2024学年高二上学期期末模拟数学试题(一)(已下线)第三章:圆锥曲线的方程章末重点题型复习-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)(已下线)专题24 抛物线的标准方程4种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)重庆市云阳县云阳高级中学校2023-2024学年高二上学期第二次月考数学试题(已下线)第3章:圆锥曲线与方程章末重点题型复习-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)(已下线)高二上学期期末考点大通关真题精选100题(2)云南省保山市腾冲市民族中学2023-2024学年高二下学期开学摸底考试数学试卷(A卷)
8 . 已知实数m,n满足
.令
,
,记动点
的轨迹为E.
(1)求E的方程,并说明E是什么曲线;
(2)过点
作相互垂直的两条直线
和
,
和
与E分别交于A、B和C、D,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656c9f0000b55609d0b4451d7a8bdca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/017488660cd2e871bf26ff3ec1745a59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183fedbd8ccd264784a57e1089613578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
(1)求E的方程,并说明E是什么曲线;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd15503ee692f8286b0312f7c6f0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495021c7da1c77e6ed1d1dd30e0be7bc.png)
您最近一年使用:0次
2023-10-07更新
|
490次组卷
|
4卷引用:云南省昆明市第二十四中学2024届高三上学期月考数学试题(一)
云南省昆明市第二十四中学2024届高三上学期月考数学试题(一)河南省郑州市第四高级中学2023-2024学年高二上学期期中数学试题(已下线)考点14 直线与圆锥曲线相交问题 2024届高考数学考点总动员【练】(已下线)第三章 圆锥曲线的方程【单元提升卷】-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
解题方法
9 . 如图,矩形
中,
分别为线段
上的动点,且满足
.点
关于原点的对称点为
,直线
与
交于点
,则点
到直线
的最小距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2770af34e98289b54d37ec725b5c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c87b8e05d61ddc69dbc02772d719d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f229da509d49cebc3ca284fd58c55b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83847bf2e9122ea6a025efd87bd535f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1748d0813461ae3151f8a07f9dda383e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/5/e7e972c5-2df4-4b47-93e8-a4d3939ed5be.png?resizew=180)
您最近一年使用:0次
2023-10-04更新
|
799次组卷
|
4卷引用:湖南省长沙市第一中学2024届高三上学期月考(三)数学试题
湖南省长沙市第一中学2024届高三上学期月考(三)数学试题辽宁省部分名校2023-2024学年高二上学期联考数学试题(已下线)重难专攻(八)圆锥曲线中的最值(范围)问题(B素养提升卷)广东省广州市天河区广州天省实验学校2023 -2024学年高三上学期中段质量检测数学试题
名校
解题方法
10 . 已知
为圆
:
上任一点,
,
,
,且满足
.
(1)求动点
的轨迹
的方程;
(2)直线
:
与轨迹
相交于
,
两点,与
轴交于点
,过
的中点且斜率为
的直线与
轴交于点
,记
,若
,求
的取值范围.
![](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/b7c95cccf9bdd483370ec3d1e45a787f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d70b4a9d6ed047b88c5b1070fbdc1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bae5e6584d7b42dbf6342be95a115fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c63c343a754e267472296435b18d80f.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8f22540e5479893885f87792ff0b36.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/ca10e14c61bf7a4b116a1e1836c98f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24a204c84905a1b2f0ace7c23f02845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
您最近一年使用:0次
2023-09-30更新
|
1236次组卷
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