名校
解题方法
1 . 已知平面上一动点
到定点
的距离比到定直线
的距离小
,记动点
的轨迹为曲线
.
(1)求
的方程;
(2)点
为
上的两个动点,若
恰好为平行四边形
的其中三个顶点,且该平行四边形对角线的交点在第一、三象限的角平分线上,记平行四边形
的面积为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7b76d897de678faaf8221bafe217d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb93b19779fab3f7a6991633933a364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3687b9de2cd647ee49c4b9b01eac438a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45bd92770adca80f9aa3d2e4b7e106a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f790a1d74e757158ccac343e5dac6af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab3e0100e6788858ab43861933dd248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab3e0100e6788858ab43861933dd248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4532e8175640973b48fa2bb4f53310.png)
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2024-04-03更新
|
1501次组卷
|
4卷引用:辽宁省八市八校2024届度高三第二次联合模拟考试数学试题
辽宁省八市八校2024届度高三第二次联合模拟考试数学试题2024届辽宁省名校联盟高考模拟卷(调研卷)数学试题(一)(已下线)专题8.4 抛物线综合【八大题型】(已下线)重难点14 圆锥曲线必考压轴解答题全归类【十一大题型】(举一反三)(新高考专用)-1
名校
解题方法
2 . 已知椭圆
:
,
的左右顶点分别为A,B,长轴长为4,点D为椭圆上与A,B不重合的点,且
.
(1)求椭圆方程;
(2)(i)一条垂直于x轴的动直线l交椭圆
于P,Q两点,当直线l与曲线
相切于点A或点B时,看作P,Q两点重合于点A或点B,求直线
与直线
交点E的轨迹
的方程;
(ii)过
的直线l与曲线
交于M,N两点,且两交点均在y轴右侧,直线
与曲线
交于G点,直线
与曲线
交于H点,记
的面积为
,记
的面积为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434249d6640b0c1a712d215cf8b83d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d535e8f64701b23064b2c6da6b1420d3.png)
(1)求椭圆方程;
(2)(i)一条垂直于x轴的动直线l交椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(ii)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f2a72c6d7780757ab065fb29f47526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f8b3d45ae1743416253d835c054456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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2024-06-12更新
|
227次组卷
|
2卷引用:黑龙江省佳木斯市第一中学2023-2024学年高三第三次模拟考试数学试题
名校
解题方法
3 . 如图,在矩形
中,
,
,
分别为边
,
的中点,
,
分别为线段
(不含端点)和
上的动点,满足
,直线
,
的交点为
,已知点
的轨迹为双曲线的一部分,则该双曲线的渐近线方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dcbfddee91a527e278d80608f0f35be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb85d28f8bdeedad66fd7ec2a561455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131e4c8344dcc29a53bd13f70eeea2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06b75fb4e379ff3b99e68f40136cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2024-01-13更新
|
361次组卷
|
6卷引用:湖南省衡阳市第八中学2024届高三上学期第一次模拟测试数学试题
湖南省衡阳市第八中学2024届高三上学期第一次模拟测试数学试题上海市行知中学2023-2024学年高二上学期期末数学试卷江西省新余市实验中学2023-2024学年高二下学期开学摸底考试数学试卷(已下线)第2章 圆锥曲线 单元综合检测(重点)-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)专题5 曲线轨迹与交点问题(已下线)专题04 圆锥曲线(六大题型+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)
名校
解题方法
4 . 双纽线是1694年被瑞士数学家雅各布·伯努利用来描述他所发现的.在平面直角坐标系
中,把到定点
和
距离之积等于
的点的轨迹称为双纽线
.已知点
是双纽线
上一点,下列说法正确的是( )
①双纽线
关于原点对称;②
;③双纽线
上满足
的点
只有两个;④
的最大值是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcb162568cb923c31c7209c8a22e4674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5500891685c5105a390f03ebcb1efcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be45dd63a0db0b7ab458f30ee6a67881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①双纽线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d8e5f5e7c86136ba521a6b29ee2752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f6bccd63572d3f37da409fda25af6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f625aa2ab29879c1df77417e9c1cf71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827bec361fa9658bc190b57633f2b5aa.png)
A.①②③ | B.①②④ | C.①② | D.①②③④ |
您最近一年使用:0次
名校
5 . 已知正方体
的棱长为2,棱
的中点为
,过点
作正方体的截面
,且
,若点
在截面
内运动(包含边界),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77bc6a7e1ace458b04b99247bca0accd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.当![]() ![]() ![]() ![]() |
B.三棱锥![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 已知在平面直角坐标系
中,
:
,
:
,平面内有一动点
,过
作
交
于
,
交
于
,平行四边形
面积恒为1.
(1)求点
的轨迹方程并说明它是什么图形;
(2)记
的轨迹为曲线
,
,当
在
轴右侧且不在
轴上时,在
轴右侧的
上一点
满足
轴平分
,且
不与
轴垂直或
是
的一条切线,求
与
,
围成的三角形的面积最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4407788e4dc88210bca71a2551d4f2f9.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/b22c9e62d7dfe7116965d5f809f54fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8565d467e55e50c9c999868ce289f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e089ac241dbeeda7d9172a394d6acb.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)记
![](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/488675b0c71bc75ccea45696c496080b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/b95cfffad86cdce753e3025437b6ef14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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2024-03-21更新
|
1095次组卷
|
3卷引用:广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)
7 . 已知点,动点
在直线
:
上,过点
且垂直于
轴的直线与线段
的垂直平分线交于点
,记点
的轨迹为曲线
.
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/299b9274e61eafb5bb2d07f8d5a70bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74625390340982140e449e07663579a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
2024-01-13更新
|
592次组卷
|
8卷引用:安徽省江淮十校2023届高三三模数学试题
安徽省江淮十校2023届高三三模数学试题重庆市南开中学校2023届高三第九次质量检测数学试题黑龙江省大庆市大庆中学2023届高三三模数学试题湖北省武汉市第六中学2022-2023学年高二下学期第四次月考数学试题安徽省淮北市树人高级中学2023-2024学年高三上学期开学检测数学试题(已下线)专题15 圆锥曲线综合广东省珠海市第一中学2024届高三上学期大湾区期末数学预测卷(五)(已下线)重难点14 圆锥曲线必考压轴解答题全归类【十一大题型】(举一反三)(新高考专用)-1
2023·全国·模拟预测
解题方法
8 . 已知椭圆
的离心率为
,
为椭圆的左、右顶点,
为椭圆的左、右焦点,
是椭圆上异于
的任意一点,过
作直线
的垂线,垂足为
,直线
交
于点
,交椭圆于
两点,△
的面积最大值为12,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
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A.![]() |
B.若![]() ![]() ![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2023·全国·模拟预测
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解题方法
9 . 如图,在棱长为2的正方体
中,
为棱
的中点,
为底面
内的一动点(含边界),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.过点![]() ![]() ![]() ![]() |
B.存在点![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.当三棱锥![]() ![]() ![]() |
您最近一年使用:0次
2023-12-24更新
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1398次组卷
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8卷引用:2024年全国高考名校名师联席命制型数学信息卷(三)
(已下线)2024年全国高考名校名师联席命制型数学信息卷(三)重庆市乌江新高考协作体2024届高三上学期高考第一次联合调研抽测数学试题广东省东莞市东华高级中学2024届高三一模数学试题重庆市第十八中学2023-2024学年高二上学期期末模拟数学试题(A卷)江西省吉安市第一中学2024届高三三模数学试题重庆市第十八中学2023-2024学年高二上学期期末数学模拟试题(已下线)模块7 空间几何篇 第2讲:立体几何的截面问题【练】(已下线)黄金卷07(2024新题型)
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10 . 如图,在棱长为2的正方体
中,已知M,N,P分别是棱
,
,
的中点,Q为平面
上的动点,且直线
与直线
的夹角为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f995d8b97b790ba7b5e934c7cbd4a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a7bcc1efb8a2ff57d64b6d057da463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
A.![]() ![]() |
B.平面![]() ![]() |
C.点Q的轨迹长度为![]() |
D.能放入由平面PMN分割该正方体所成的两个空间几何体内部(厚度忽略不计)的球的半径的最大值为![]() |
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2023-12-18更新
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3053次组卷
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7卷引用:广东省广州市2024届高三上学期调研测试数学试题(B)
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