名校
解题方法
1 . 在平面上,定点
、
之间的距离
,曲线C是到定点
、
距离之积等于
的点的轨迹.以点
、
所在直线为x轴,线段
的中垂线为y轴,建立直角坐标系.已知点
是曲线C上一点,下列说法中正确的有( )
①曲线C是中心对称图形;
②曲线C上的点的纵坐标的取值范围是
;
③曲线C上有两个点到点
、
距离相等;
④曲线C上的点到原点距离的最大值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8bfae3435fcf141dcdd83e1ad4f1b6d.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/7b2d4ff799e2f87b3786a04c83f63d5d.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/bfd789f3b1f753a6608e4ca80feb275b.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/caf0d139c9810361b4971904a943856b.png)
①曲线C是中心对称图形;
②曲线C上的点的纵坐标的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b954290ebcecbdbeed83b32fc5ce81.png)
③曲线C上有两个点到点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
④曲线C上的点到原点距离的最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8bfae3435fcf141dcdd83e1ad4f1b6d.png)
A.①② | B.①②④ | C.①②③④ | D.①③ |
您最近一年使用:0次
2023-01-13更新
|
506次组卷
|
5卷引用:上海市进才中学2022-2023学年高二上学期期末数学试题
上海市进才中学2022-2023学年高二上学期期末数学试题(已下线)核心考点04抛物线、曲线与方程(3)(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)(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)
2 . 已知正方体
的边长为2,
为正方体内(包括边界)上的一点,且满足
,则下列说正确的有( )
![](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/8374a540227b8851ddfff976f73afe04.png)
A.若![]() ![]() ![]() ![]() |
B.过![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
3 . 已知正四面体ABCD,M,N分别是棱AB,CD上的点,且满足
,直线MN的轨迹为曲面
.P,Q,R分别为AB,AC,AD的中点,曲面
与平面PQR的交线为圆锥曲线的一部分,该圆锥曲线的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdc9f4a99b567a6ee4be3943beeddca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
您最近一年使用:0次
名校
4 . 已知动圆Q过点
,且与直线
相切,记动圆Q的圆心轨迹为
,过l上一动点D作曲线
的两条切线,切点分别为A、B,直线
与y轴相交于点F,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42502a5730e1930d77d7100d1e34707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() ![]() | B.直线![]() |
C.![]() | D.以![]() ![]() |
您最近一年使用:0次
2022-11-28更新
|
831次组卷
|
4卷引用:广东省百校联盟2023届高三上学期综合能力测试(三)数学试题
解题方法
5 . 如图,已知四面体
,
和
是边长为2的正三角形,
,
是该四面体表面及其内部的动点.若
,
,则点
轨迹的长度为______ ;若
在
内(含边界)且
,则点
轨迹的长度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18120a244d3a1f9c1688bf53eb2ad775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed66431681da1db8f7cb0f40cd19201.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/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/cdaf4622-4033-4371-acee-eac803a1bfba.png?resizew=157)
您最近一年使用:0次
2022-11-23更新
|
440次组卷
|
2卷引用:辽宁省名校联盟2022-2023学年高三上学期11月份联合考试数学试题
6 . 已知椭圆
,
的离心率相同.点
在椭圆
上,
、
在椭圆
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/5f2eb408-6fd8-4e7d-9bb3-bc7b6dc6159b.png?resizew=207)
(1)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/517cc345e3e8a3c9405c0e240d8ca011.png)
求点
的轨迹方程;
(2)设
的右顶点和上顶点分别为
、
,直线
、
分别是椭圆
的切线,
、
为切点,直线
、
的斜率分别是
、
,求
的值;
(3)设直线
、
分别与椭圆
相交于
、
两点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d424a04295723f4a974c4428950bd06.png)
若
是
中点,求证:
、
、
三点共线(
为坐标原点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c845a5c4ab840aceef677fbe2b0cf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ecc27514f0e4af04106cf02c40c3b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/5f2eb408-6fd8-4e7d-9bb3-bc7b6dc6159b.png?resizew=207)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/517cc345e3e8a3c9405c0e240d8ca011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05250abe6da85eb0b555948d7dbaf317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4c8b6a3a27a6713d62b8206151f838.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.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/7d424a04295723f4a974c4428950bd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05250abe6da85eb0b555948d7dbaf317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
2022-11-19更新
|
460次组卷
|
2卷引用:上海市杨浦区复旦大学附属中学2022-2023学年高二上学期期中数学试题
名校
7 . 已知正方体
的棱长为1,点P为侧面
内一点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.当点P到平面ABCD的距离等于到直线![]() |
D.当![]() |
您最近一年使用:0次
2022-11-09更新
|
1143次组卷
|
6卷引用:江苏省南京市2022-2023学年高二上学期期中数学试题
名校
解题方法
8 . 平面内一动点
到定直线
的距离,是它与定点
的距离的两倍.
(1)求点
的轨迹方程
;
(2)过
点作两条互相垂直的直线
,
(直线
不与
轴垂直).其中,直线
交曲线
于
,
两点,直线
交曲线
于
,
两点,直线
与直线
交于点
,若直线
,
,
的斜率
,
,
构成等差数列,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b0b7dc61346c291554562762fd0558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f998f87124daa3d26643725676b15c97.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9eeee83b4b7c6ceac7828ff534ce15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5d04fbdee890603b0b3621037f3c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd6a1d6fab318824426e52464a575e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44368a1c81e2bb3608b412ac0c44f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546a035918f025942ca99b9ffebd8eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
您最近一年使用:0次
2022-10-20更新
|
697次组卷
|
4卷引用:贵州省六校联盟2023届高三上学期高考实用性联考(一)数学(理)试题
贵州省六校联盟2023届高三上学期高考实用性联考(一)数学(理)试题贵州省六校联盟2023届高三上学期高考实用性联考(一)数学(文)试题内蒙古自治区赤峰市赤峰二中2022-2023学年高三上学期第二次月考理科月考数学试题(已下线)专题32 一类与斜率和、差、商、积问题的探究-1
9 . 在平面直角坐标系
中, 设点
, 点
与
两点的距离之和为
为一动点, 点
满足向量关系式:
.
(1)求点
的轨迹方程
;
(2)设
与
轴交于点
(
在
的左侧), 点
为
上一动点 (且不与
重合). 设直线
轴与直线
分别交于点
,取
,连接
,证明:
为
的角平分线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3933c6a5b045c5e8f0a33ad569b76c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba9159195d6006db96d78578b7f1cfc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440981bbf50be4ff25fb266f8b968c80.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d687f47eed34e5a59e557f6aacf433d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf2130848c57fdbb994e41f107329b3.png)
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2卷引用:云南师范大学附属中学2023届高三上学期适应性月考卷(三)数学试题
名校
解题方法
10 . 若正四棱柱
的底面棱长为4 ,侧棱长为3 ,且
为棱
的靠近点
的三等分点,点
在正方形
的边界及其内部运动,且满足
与底面
的所成角
,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/6/27/3010367002787840/3011755104649216/STEM/ce1c1f9450e549cbb80270b07c343ec2.png?resizew=270)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6628d0bd96fb5bef05eaeb9ab71529ea.png)
![](https://img.xkw.com/dksih/QBM/2022/6/27/3010367002787840/3011755104649216/STEM/ce1c1f9450e549cbb80270b07c343ec2.png?resizew=270)
A.点![]() ![]() |
B.四面体![]() ![]() |
C.有且仅有一个点![]() ![]() |
D.线段![]() ![]() |
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4卷引用:浙江省金华十校2021-2022学年高一下学期期末数学试题
浙江省金华十校2021-2022学年高一下学期期末数学试题重庆市北碚区2023届高三上学期10月月度质量检测数学试题(已下线)期末专题04 立体几何小题综合-【备战期末必刷真题】浙江省宁波市奉化区九校联考2022-2023学年高二下学期期末模拟数学试题