1 . 设A,B分别是直线
和
上的动点,且
,设O为坐标原点,动点G满足
.
(1)求点G运动的曲线C的方程;
(2)直线
与曲线C交于M,N两点,O为坐标原点,当k为何值,
恒为定值,并求此时
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91a18f8751aa1008f1e43516a588207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f899446faaf4935179eec468e5943b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd2d9dc6872ed14cc33ce6619c59a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c2edbce7e34726aaeb2bb5da100004.png)
(1)求点G运动的曲线C的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327a8132cb929667c033a3c20bd9c67c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4de13a47637548ce5594ed8d64dec0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
您最近一年使用:0次
2022-06-14更新
|
1720次组卷
|
5卷引用:湖南省邵阳市邵东创新实验学校2023-2024学年高二上学期期中数学试题
(已下线)湖南省邵阳市邵东创新实验学校2023-2024学年高二上学期期中数学试题辽宁省渤海大学附属高级中学2022届高三考前测试数学试题(已下线)专题24 圆锥曲线中的存在性、探索性问题 微点2 圆锥曲线中的探索性问题四川省泸县第五中学2022-2023学年高二下学期期中数学(文)试题四川省泸县第五中学2022-2023学年高二下学期期中数学(理)试题
名校
解题方法
2 . 平面直角坐标系内有一定点
,定直线
,设动点P到定直线的距离为d,且满足
.
(1)求动点P的轨迹方程;
(2)直线
过定点Q,与动点P的轨迹交于不同的两点M,N,动点P的轨迹与y的负半轴交于A点,直线
分别交直线
于点H、K,若
,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e1a85a657231ef717809d5a839ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b867b63257cf7aad2f9416809e0f406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c62f9f4f679ba8ac4ca1a048b114c6.png)
(1)求动点P的轨迹方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0d599c13251dad7d388f6b0e6893aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d42cb68c5c877a455ba7ac0a6b6a651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92002afa0b414eae387a91207c629398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb0b06f88054d4f432413b64c00ead5.png)
您最近一年使用:0次
2022-06-01更新
|
1839次组卷
|
4卷引用:湖南省长沙市明德中学2022-2023学年高三上学期入学考试数学试题
湖南省长沙市明德中学2022-2023学年高三上学期入学考试数学试题广东省2022届高三模拟押题卷(三)数学试题(已下线)专题26 求动点轨迹方程 微点2 定义法求动点的轨迹方程四川省绵阳中学2023届高三上学期1月模拟检测文科数学试题
名校
解题方法
3 . 在平面直角坐标系
中,动点
到直线
的距离和点
到点
的距离的比为
,记点
的轨迹为
.
(1)求
的方程;
(2)若不经过点
的直线
与
交于
,
两点,且
,求△
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65ee712a3601f42db09c023e70710e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)若不经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.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/ebb3873635a1c1815637c916fe0430c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
您最近一年使用:0次
2022-05-06更新
|
1242次组卷
|
3卷引用:湖南省株洲市南方中学2022-2023学年高三上学期9月月考数学试题
解题方法
4 . 已知圆
与圆
的公共点的轨迹为曲线
.
(1)求
的方程;
(2)已知点
,过
的直线与曲线
交于
两点.直线
与直线
分别交于不同的两点
,证明:以
为直径的圆过点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8b4fe3d22d3bc9b609ed7d237495fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933c46a438d6ec4410212dfb32d07e82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
您最近一年使用:0次
名校
解题方法
5 . 平面内两定点F1(
,0),F2(
,0),点O为坐标原点,动点P满足F2P的中点E在⊙O:
上,点Q在F1P上且
.
(1)求动点Q的轨迹C的方程;
(2)过点D(3,0)分别作两条直线与轨迹C交于点A,点B.线段DA的中点为M,线段DB的中点为N,若OM⊥ON,求证:直线AB过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0d7704614f7106d3e838c5c121b8f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08227ca941898eb34941f446ca8b1de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2970ece1dff70d1109579c5b87f035.png)
(1)求动点Q的轨迹C的方程;
(2)过点D(3,0)分别作两条直线与轨迹C交于点A,点B.线段DA的中点为M,线段DB的中点为N,若OM⊥ON,求证:直线AB过定点.
您最近一年使用:0次
2022-03-19更新
|
596次组卷
|
2卷引用:湖南省长沙市第一中学2022届高三下学期月考(八)数学试题
解题方法
6 . 在平面直角坐标系
中,已知圆
,点P在圆上,过点P作x轴的垂线,垂足为
是
的中点,当P在圆M上运动时N形成的轨迹为C.
(1)求C的轨迹方程;
(2)若点
,试问在x轴上是否存在点M,使得过点M的动直线
交C于
两点时,恒有
?若存在,求出点M的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5240a75b910e7d57c991cd574ee896e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba980084511f24e501994ca60cb19273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(1)求C的轨迹方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d30a439925d5b4ab014cdf0fdd4f82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6eb1487edf0fc38f2ca7f40979d99a6.png)
您最近一年使用:0次
解题方法
7 . 设圆
的圆心为
﹐直线l过点
且与x轴不重合,直线l交圆
于A,B两点.过
作
的平行线交
于点P.
(1)求点P的轨迹方程;
(2)设点P的轨迹为曲线E,直线l交E于M,N两点,C在线段
上运动,原点O关于C的对称点为Q,求四边形
面积的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714df7f0c804617e1c8832d2e91b496a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c23080907d8cc5c0ffdee2b0ced6865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
(1)求点P的轨迹方程;
(2)设点P的轨迹为曲线E,直线l交E于M,N两点,C在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe3174b77e624cd0fdb730bbe00322f.png)
您最近一年使用:0次
8 . 长方体
中,
,
,
,
为侧面
内(含边界)的动点,且满足
,则四棱锥
体积的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7034287e0860c93c33e28a79039f2c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 已知点A(
,0),点C为圆B:
(B为圆心)上一动点,线段AC的垂直平分线与直线BC交于点G.
(1)设点G的轨迹为曲线T,求曲线T的方程;
(2)若过点P(m,0)(
)作圆O:
的一条切线l交(1)中的曲线T于M、N两点,求△MNO面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553360f0476d7533adfae3d0e862946b.png)
(1)设点G的轨迹为曲线T,求曲线T的方程;
(2)若过点P(m,0)(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
您最近一年使用:0次
2022-01-29更新
|
654次组卷
|
2卷引用:湖南师范大学附属中学2021-2022学年高二上学期期末数学试题
名校
10 . 已知圆
,点
,
是圆
上一动点,若线段
的垂直平分线与线段
相交于点
.
(1)求点
的轨迹方程;
(2)已知
为点
的轨迹上三个点(
不在坐标轴上),且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a7360317a18a25bcb3c9042c4570f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f36374ce95a4945d0e58264c2b271f.png)
![](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/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf0edea792798049cd728af69f74e19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
您最近一年使用:0次
2022-01-18更新
|
867次组卷
|
3卷引用:湖南省邵阳市2021-2022学年高三上学期第一次联考数学试题