名校
解题方法
1 . 已知圆
和点
,动圆
经过点
,且与圆
内切.
(1)求动圆的圆心
的轨迹
的方程;
(2)设点
关于点
的对称点为
,直线
与轨迹
交于
、
两点,若
的面积为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352611d80410dad2985ab5f5f923db32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求动圆的圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc3827b09caea067fe3b4617b655fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea8578ed02bbdaa1d8838483dbae5cc.png)
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f29319f8bcfaa1b2cf21a930146431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2021-06-10更新
|
501次组卷
|
4卷引用:重庆市2021届高三高考数学第三次联合诊断检测试题
重庆市2021届高三高考数学第三次联合诊断检测试题重庆市实验中学2021-2022学年高二上学期第二次阶段性测试数学试题(已下线)3.1.2 椭圆的简单几何性质-2021-2022学年高二数学同步速效提升练(人教A版2019选择性必修第一册)【学科网名师堂】安徽省芜湖市2021-2022学年高二上学期期中联考数学试题
2 . 如图,已知点
,
以线段
为直径的圆内切于圆
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/c05df6c2-92a5-4016-b385-51bb9cbef560.png?resizew=187)
(1)证明
为定值,并写出点G的轨迹E的方程;
(2)设点A,B,C是曲线E上的不同三点,且
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be19f9ec16fc625d1e4e87496c08921c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/c05df6c2-92a5-4016-b385-51bb9cbef560.png?resizew=187)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3374c44598a5a16275d07f76c6eb385.png)
(2)设点A,B,C是曲线E上的不同三点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533aec812673c602f025e1a52b9c60ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2020-12-01更新
|
635次组卷
|
4卷引用:重庆市国维外国语学校2020-2021学年高二上学期第三次月考数学试题
重庆市国维外国语学校2020-2021学年高二上学期第三次月考数学试题湖南省衡阳市船山英文学校2020-2021学年高三上学期大联考数学试题陕西省西安中学2021届高三下学期第五次模拟数学(文)试题(已下线)专题29 圆锥曲线求定值七种类型大题100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)
名校
3 . 动点
分别与两定点
,
连线的斜率的乘积为
,设点
的轨迹为曲线
,已知
,
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993769b494e12c21dff0ee7c53a4a49f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7291b3d921f595f28960abcdce6dfbed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e1464ae5e241f74333a5381334acb9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d725494ad76dc0ef160cf05af0f1d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b9e6530b912f758f9facbae31351c4.png)
A.2 | B.6 | C.![]() | D.10 |
您最近一年使用:0次
解题方法
4 . 设
两点的坐标分别为
,直线
相交于点
,且它们斜率之积为
.
(1)求点
的轨迹方程
;
(2)若斜率为
(其中
)的直线
过点
,且与曲线
交于点
,弦
的中点为
,
为坐标原点,直线
与曲线
交于点
,求四边形
的面积
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7df24de03ba49795a0d2fbf7f474acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a77aa6c27acfffcc601d9ca7e6d4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/765f45c05c1acd8af20d411bdf423ded.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0878af1501b3447c5dc33758fd290b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4cd68cc82e90a5e2049a7ea3171b84.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/65e92eac740953aa383be636ea90fd47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
名校
解题方法
5 . 已知
过点
,且与
内切,设
的圆心
的轨迹为
,
(1)求轨迹C的方程;
(2)设直线
不经过点
且与曲线
交于点
两点,若直线
与直线
的斜率之积为
,判断直线
是否过定点,若过定点,求出此定点的坐标,若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fb3c76710654d9997d3ed6ebb191fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e24a62626ece4e4e239756e3980debf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求轨迹C的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fab7face5f8236308525bff9c68d01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd8cb171425253834dfd7fa1a9da9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-05-04更新
|
609次组卷
|
3卷引用:重庆市九龙坡区育才中学校2024届高三上学期第三次联考复习数学试题
6 . 设
为坐标原点,动点
在椭圆
上,过
作
轴的垂线,垂足为
,点
满足
.(Ⅰ)求点
的轨迹方程
;
(Ⅱ)过
的直线
与点
的轨迹交于
两点,过
作与
垂直的直线
与点
的轨迹交于
两点,求证:
为定值.
![](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/6205da5e1d2730ee0b3de8bca3e29f5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/0ec0811a4f65c624380eef73b8416243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c29a7e8eea08197bf53164a560bee58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f5af055f303c24d94314efcc0f616a.png)
您最近一年使用:0次
2018-01-25更新
|
1229次组卷
|
4卷引用:重庆市凤鸣山中学2021届高三下学期第一次月考数学试题
重庆市凤鸣山中学2021届高三下学期第一次月考数学试题辽宁省沈阳市2018届高三教学质量监测(一)数学理试题(已下线)第39讲 斜率和积问题与定点定值问题-2022年新高考数学二轮专题突破精练广东省江门市第一中学2023届高三下学期2月月考数学试题
名校
7 . 设D是圆O:x2+y2=16上的任意一点,m是过点D且与x轴垂直的直线,E是直线m与x轴的交点,点Q在直线m上,且满足2|EQ|
|ED|.当点D在圆O上运动时,记点Q的轨迹为曲线C.
(1)求曲线C的方程.
(2)已知点P(2,3),过F(2,0)的直线l交曲线C于A,B两点,交直线x=8于点M.判定直线PA,PM,PB的斜率是否依次构成等差数列?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e589def3e7fe21b601bc6d5144073202.png)
(1)求曲线C的方程.
(2)已知点P(2,3),过F(2,0)的直线l交曲线C于A,B两点,交直线x=8于点M.判定直线PA,PM,PB的斜率是否依次构成等差数列?并说明理由.
您最近一年使用:0次
2019-05-07更新
|
907次组卷
|
10卷引用:重庆市第十一中学2020届高三下学期6月月考数学(理)试题
重庆市第十一中学2020届高三下学期6月月考数学(理)试题【市级联考】广西南宁市2019届高三毕业班第一次适应性测试数学(理科)试题【市级联考】广西南宁市2019届高三毕业班第一次适应性测试数学(文)试题【市级联考】湖南省湘潭市2019届高三下学期第二次模拟考试数学(文)试题【市级联考】湖南省湘潭市2019届高三下学期第二次模拟考试数学(理)试题【市级联考】湖南省长沙市2019届高三下学期第二次模拟考试数学(理)试题【市级联考】湖南省长沙市2019届高三下学期第二次模拟考试数学(文)试题【市级联考】辽宁省辽阳市2019届高三下学期一模数学(理科)试题2020年普通高等学校招生全国统一考试理科数学样卷(五)2020年普通高等学校招生全国统一考试 文科数学样卷(五)
8 . 已知圆
与x轴的正半轴交于点A,过圆O上任意一点P作x轴的垂线,垂足为Q,线段PQ的中点的轨迹记为曲线
,设过原点O且异于两坐标轴的直线与曲线
交于B,C两点,直线AB与圆O的另一个交点为M,直线AC与圆O的另一个交点为N,设直线AB,AC的斜率分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f67daeddff2e805bf34d43e629d959.png)
.
(1)求
的值;
(2)判断
是否为定值?若是,求出此定值;否则,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f67daeddff2e805bf34d43e629d959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509bb54bce15c0d97ca43f2abd2c6852.png)
您最近一年使用:0次
2020-02-07更新
|
666次组卷
|
2卷引用:2020届重庆市高三上学期期末测试卷理科数学( 一诊康德卷)
名校
解题方法
9 . 动点
到定点
的距离与到定直线
的距离之比为定值
.
(1)求动点
的轨迹方程:
(2)若直线
与动点
的轨迹交于不同的两点
,
,且线段
被直线
平分,求直线
的斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2347bec7975dab2b8bce2fd19b1237d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de72a5190834f5dbe895596656c038b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7256fdf141b049c0ad98234f48db84a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
10-11高二上·福建厦门·期中
名校
解题方法
10 . 如图所示,已知圆
,定点
,
为圆上一动点,点
在
上,点
在
上,且满足
,
,点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)若过定点
的直线交曲线
于不同的两点
、
(点
在点
、
之间),且满足
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5102dc1b3f322035132dffb88948f45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8950c7bc835103d52ceffab14b6b31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75bdc3080df7ad047adc88916b8784d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5658ac14d657456ad90f185afdec22ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/70b07f6d-debb-49d7-b091-6697726d92ab.png?resizew=176)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce421051739231bcd982a403097ca41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac2165a743e45123e1c9796a7cba2346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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