1 . 如图,圆
,圆
,动圆
与圆
外切于点
,与圆
内切于点
,记圆心
的轨迹为曲线
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f09301f91879129399c1ba45635f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3e7ea39906456429384362b6d037ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() |
D.曲线![]() ![]() ![]() |
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2 . 若复数
的实部为4,则点
的轨迹是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296ff2a951b1289afab987fadb46f43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
A.短轴长为4的椭圆 | B.实轴长为4的双曲线 |
C.长轴长为4的椭圆 | D.虚轴长为4的双曲线 |
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2024-04-24更新
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233次组卷
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3卷引用:四川省雅安市2024届高三下学期4月联考数学(理)试题
3 . 平面直角坐标系中,等边
的边长为2,M为
中点,B,C分别在射线
,
上运动,记M的轨迹为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79301e3963cf05b1ac7c249749420475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 如图,圆
的半径为4,
是圆内一个定点且
是圆
上任意一点,线段
的垂直平分线
和半径
相交于点
,点
在圆上运动.
的轨迹;
(2)当
时,证明:直线
与点
形成的轨迹相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912708d9c4feb53232e8c9db822ba694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcfaca9396f85c0137b534903321fcbe.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)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1987787c165f519b146752aba8b2f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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2024高二上·全国·专题练习
5 . 已知圆
,
,动圆
与
,
都相切,则动圆C的圆心轨迹E的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1daeb4296576f4728bf387dbfa726874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7feb61317950d7b6abc1464f309361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
6 . 圆
与
的位置关系为______ ;与圆
,
都内切的动圆圆心的轨迹方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f137a4a18b73e7286db82588ba2fd975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5093d0fbea77573dd366f6a8361bbc2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2024-02-06更新
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716次组卷
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5卷引用:河南省信阳市固始县2023-2024学年高二上学期期末考试数学试卷
7 . 已知△ABC的两个顶点坐标分别是
和
,边AB,AC所在直线的斜率的乘积是
,则顶点A的轨迹方程为_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23b9fc6ffcd8047efb5e7748fb7e4ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df957b06efbd4bb374bf2aa248ca43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b889efe020137b112bfafaa8e0becda4.png)
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8 . 在圆
上任取一点
,过点
作
轴的垂线段
,垂足为
.当点
在圆上运动时,线段
的中点
的轨迹是椭圆
.
(1)求该椭圆
的方程.
(2)法国数学家加斯帕尔·蒙日(1746—1818)发现:椭圆上任意两条互相垂直的切线的交点,必在一个与椭圆同心的圆上,称此圆为该椭圆的“蒙日圆”.若椭圆
的左、右焦点分别为
为椭圆
上一动点,直线
与椭圆
的蒙日圆相交于点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1ab6c10bc0a8bfbdc3b4824c2de1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1ab6c10bc0a8bfbdc3b4824c2de1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求该椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)法国数学家加斯帕尔·蒙日(1746—1818)发现:椭圆上任意两条互相垂直的切线的交点,必在一个与椭圆同心的圆上,称此圆为该椭圆的“蒙日圆”.若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ed463bf16c78a4bbb9d3acff922afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.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/37a29c6bb540fcb90f8f29b3da633c07.png)
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解题方法
9 . 在平面直角坐标系xOy中,动点M到点
的距离与到直线
的距离之比为
.
(1)求动点M轨迹W的方程;
(2)过点F的两条直线分别交W于A,B两点和C,D两点,线段AB,CD的中点分别为P,Q.设直线AB,CD的斜率分别为
,
,且
,试判断直线PQ是否过定点.若是,求出定点的坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求动点M轨迹W的方程;
(2)过点F的两条直线分别交W于A,B两点和C,D两点,线段AB,CD的中点分别为P,Q.设直线AB,CD的斜率分别为
![](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/a745c2da749f30fcf58edf0821f7cb04.png)
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2024-01-18更新
|
1051次组卷
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4卷引用:山东省济南市2024届高三上学期期末学习质量检测数学试题
山东省济南市2024届高三上学期期末学习质量检测数学试题(已下线)专题18 圆锥曲线高频压轴解答题(16大核心考点)(讲义)-1(已下线)广东省佛山市第一中学2024届高三上学期第二次调研数学试题变式题17-22广东省佛山市第一中学2024届高三上学期第二次调研数学试题
10 . 在平面直角坐标系
中,点A,B分别在x轴,y轴上运动,且
,动点P满足
.
(1)求动点P的轨迹C的方程;
(2)设点M,N在曲线C上,O为坐标原点,设直线
,
的斜率分别为
,
,且
,试判断
的面积是否为定值?若为定值,求出该定值;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529b4836786aca156de325464ea2ecd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eee4dbf8d1be07b2f95ac0d26a9262f9.png)
(1)求动点P的轨迹C的方程;
(2)设点M,N在曲线C上,O为坐标原点,设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.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/02324abee955451054237a932230500a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
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2024-01-14更新
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5卷引用:陕西省宝鸡市2024届高三上学期高考模拟检测(一)数学(理)试题
陕西省宝鸡市2024届高三上学期高考模拟检测(一)数学(理)试题重庆市九龙坡区重庆实验外国语学校2024届高三下学期入学测试数学试题(已下线)专题06 直线与圆、椭圆方程(分层练)(三大题型+12道精选真题)宁夏银川市第二中学2024届高三第一次模拟考试数学(理)试题内蒙古自治区呼和浩特市剑桥中学2023-2024学年高二下学期第一次(3月)月考数学试题