1 . 如图,已知动圆
过点
,且与圆
内切于点
,记动圆圆心
的轨迹为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/8411102c-95e7-4a51-9428-c933610bf767.png?resizew=148)
(1)求
的方程;
(2)过点
的直线
交
于
、
两点,是否存在实数
,使得
恒成立?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23c80a66812d5f80beb5013bc0ec14f.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/8411102c-95e7-4a51-9428-c933610bf767.png?resizew=148)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bc8a05973277d45cf7e0aa992d47dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2022-12-11更新
|
465次组卷
|
2卷引用:山东省菏泽市定陶区定陶区明德学校(山大附中实验学校)2022-2023学年高二上学期期中数学试题
名校
解题方法
2 . 已知定点
,圆
(N为圆心,O为坐标原点),点Q为圆N上动点,线段MQ的垂直平分线交NQ于点P,记点P的轨迹为曲线C,过N的直线l与曲线C交于A,B两点.
![](https://img.xkw.com/dksih/QBM/2022/2/17/2918488236072960/2935556476329984/STEM/e158d31fc42648a8ab0c5e09277b98bd.png?resizew=176)
(1)求曲线C的方程;
(2)点T在线段AB上,且
,点B关于原点的对称点为R,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cf8af6e62058cc4e2d83d5da7f4c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497ea0a7013ccf7ea9c0f41814c2caa5.png)
![](https://img.xkw.com/dksih/QBM/2022/2/17/2918488236072960/2935556476329984/STEM/e158d31fc42648a8ab0c5e09277b98bd.png?resizew=176)
(1)求曲线C的方程;
(2)点T在线段AB上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040ec19314fd701f070821163329a00d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef7331580fcf101f517731009322999.png)
您最近一年使用:0次
3 . 已知圆
,
,点P是圆A上的动点,线段
的中垂线交
于点Q.
(1)求动点Q的轨迹方程.
(2)若点
,
,过点B的直线与点Q的轨迹交于点S,N,且直线
、
的斜率
,
存在,求证:
为常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ab893f52cdf7be72127b9bd63c09fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2d7ff2b15c4e93fe6b92baca3c76d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
(1)求动点Q的轨迹方程.
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a2b8b43e1fe82fc439d145e91b860c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33accbbbde2d8e87780401f5b9c88c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77e9c89b7275b0c1a9af5c9a72e5968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d1b0f22047ec4620cd0374598fd9e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ff131c92aa9e10f696d374216cdcf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca345937331911db10bb2c71ea5831a.png)
您最近一年使用:0次
4 . 设圆
的圆心为
,直线
过点
且与
轴不重合,
交圆
于
、
两点,过
作
的平行线交
于点
,记点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过坐标原点的直线交曲线
于
、
两点,点
在第一象限,
轴,垂足为
,连接
并延长交曲线
于点
.证明:
是直角三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c05aaf9061b1219c17902f2f11f9ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a64d2e963e29c2c691bb297ec30d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)过坐标原点的直线交曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f7e98fa4da2def9eebd11a349b83e87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360496a4f5cc8a5faca5e089ae4f9531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4ee479000026b54146a5c6097dd6f4.png)
您最近一年使用:0次
5 . 设圆
的圆心为
,点
,点
为圆上动点,线段
的垂直平分线与线段
交于点
,设点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)若直线
与曲线
交于点
,
,与圆
:
切于点
,问:
是否为定值?若为定值,求出该定值;若不为定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cad81c6d332972ca8a013268b18d159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7c27cd93e4f474de152d003419f6f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c018b37259f3ead2ab2d94bd744f44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae626b30192bba5c433d399bba65411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9486e4e76ff07c6c47091e0e4b8bcd7d.png)
您最近一年使用:0次
2021-02-04更新
|
1011次组卷
|
7卷引用:山东省枣庄市2020-2021学年高二上学期期末数学试题
山东省枣庄市2020-2021学年高二上学期期末数学试题(已下线)卷14 选择性必修第一册高二上期中考试 总复习检测5(难)-2021-2022学年高二数学单元卷模拟(易中难)(2019人教A版选择性必修第一册+第二册)福建省福州市八县(市)协作校2021-2022学年高二上学期期中联考数学试题广东省深圳市南山区2021-2022学年高二上学期期末数学试题黑龙江省牡丹江市第二高级中学2022-2023学年高二上学期期中数学试题河北省石家庄二中教育集团2022-2023学年高二上学期期末四校联考数学试题重庆市万州国本中学校2022-2023学年高二上学期期末数学试题
解题方法
6 . 已知P是圆
上任意一点,
,线段
的垂直平分线与半径
交于点Q,当点P在圆
上运动时,记点Q的轨迹为曲线C.
(1)求曲线C的方程;
(2)记曲线C与x轴交于A,B两点,在直线
上任取一点
,直线
,
分别交曲线C于M,N两点,判断直线
是否过定点,若是,求出该定点的坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0430d333cd603bc096ca3cb592ab6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
(1)求曲线C的方程;
(2)记曲线C与x轴交于A,B两点,在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ccc436dfccfff55e4c75cb0386f672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98c4b3f3fe826e124ca7d199d4ca4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817a419430d9951cbdb89b657b21bcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
7 . 在平面直角坐标系
中,圆
的圆心为
.已知点
,且
为圆
上的动点,线段
的中垂线交
于点
.
(1)求点
的轨迹方程;
(2)设点
的轨迹为曲线
,若四边形
的四个顶点都在曲线
上,对角线
,
互相垂直并且它们的交点恰为点
,求四边形
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c66e89fbb623bba218b16b3672a79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fb572a6f07dcade5332bea766020f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77ce31833750a319b3c2db7837a110d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a354c472e3de0d03a4d288bb7b62a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
8 . 设A是圆O:x2+y2=16上的任意一点,l是过点A且与x轴垂直的直线,B是直线l与x轴的交点,点Q在直线l上,且满足4|BQ|=3|BA|.当点A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)已知直线y=kx﹣2(k≠0)与曲线C交于M,N两点,点M关于y轴的对称点为M′,设P(0,﹣2),证明:直线M′N过定点,并求△PM′N面积的最大值.
(1)求曲线C的方程;
(2)已知直线y=kx﹣2(k≠0)与曲线C交于M,N两点,点M关于y轴的对称点为M′,设P(0,﹣2),证明:直线M′N过定点,并求△PM′N面积的最大值.
您最近一年使用:0次
2020-01-10更新
|
389次组卷
|
3卷引用:山东省淄博市部分学校2018-2019学年高二上学期期末考试数学试题