名校
解题方法
1 . 在平面直角坐标系xOy中,已知圆心在原点的圆C与直线l1:
相切,动直线
交圆C于A,B两点,交y轴于点M.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/b6234dd1-1160-457b-b09e-8fa11f25feff.png?resizew=159)
(1)求圆C的方程;
(2)求实数k、m的关系;
(3)若点M关于O的对称点为N,圆N的半径为
.设D为AB的中点,DE,DF与圆N分别相切于点E,F,求
的最小值及
取最小值时m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bab7b913a04839bb9d4f1d5c8ce64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f44c9010af5e7b8c487b125dd053d35.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/b6234dd1-1160-457b-b09e-8fa11f25feff.png?resizew=159)
(1)求圆C的方程;
(2)求实数k、m的关系;
(3)若点M关于O的对称点为N,圆N的半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73ac18a11fd10f330c2f43a013a9638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c962fe4f47732b8e6e83d17ff2b9af13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c962fe4f47732b8e6e83d17ff2b9af13.png)
您最近一年使用:0次
2 . 已知圆
,点
在抛物线
上,
为坐标原点,直线
与圆
有公共点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/cdb6505e-6f3c-4e64-b61d-cfa226e38b3a.png?resizew=235)
(1)求点
横坐标的取值范围;
(2)如图,当直线
过圆心
时,过点
作抛物线的切线交
轴于点
,过点
引直线
交抛物线
于
两点,过点
作
轴的垂线分别与直线
交于
,求证:
为
中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d937c7cf1f0724d7d126533e49be4114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/cdb6505e-6f3c-4e64-b61d-cfa226e38b3a.png?resizew=235)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)如图,当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ce799db1630af8c8112fad754ee96b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
您最近一年使用:0次
2019-07-10更新
|
558次组卷
|
2卷引用:浙江省舟山市2018-2019学年高二下学期期末数学试题
解题方法
3 . 已知直线
、
与曲线
分别相交于点
、
和
、
,我们将四边形
称为曲线
的内接四边形.
(1)若直线
和
将单位圆
分成长度相等的四段弧,求
的值;
(2)若直线
,
与圆
分别交于点
、
和
、
,求证:四边形
为正方形;
(3)求证:椭圆
的内接正方形有且只有一个,并求该内接正方形的面积.
![](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/87b6247b1fd8f53318489696368d7587.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839fe3fc3c8f825b040fb01da9d76df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa941aa5d428f5d78ec3f281464f826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69c0979b1f101dcde663c38f52a09b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f86faa8cedab85e739ced46d705de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1afb06047f96fecf3315242963770e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78517f1ddb423a9f6ec8ea56fb8c547d.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)求证:椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962840f570c741cdec23a455ef126c51.png)
您最近一年使用:0次
名校
4 . 已知圆
,
为圆内一点,
为圆上的动点,且
,
是
的中点.
(1)求点
的轨迹方程;
(2)过点
的直线
与点
的轨迹交于
两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259e9a874ba8a4fbc027e01699a81d8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222ed48baf754fd0f7b8191e5becb98f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab4cf09670861e61d67cbe70bb149a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9121702c83ef9864c05a2e666f4d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc601d6a5f90568d8e42238f00ca2ecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/317d7ac04c9cf58ee1503f1a1bf9e3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcef5c4d2ecca9ce35fd9ed7b6a36852.png)
您最近一年使用:0次
名校
5 . 在平面直角坐标系
中,已知圆
的方程为
,
点的坐标为
.
(1)求过点
且与圆
相切的直线方程;
(2)过点
任作一条直线
与圆
交于不同两点
,
,且圆
交
轴正半轴于点
,求证:直线
与
的斜率之和为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84269a13118a599708926a24c53d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1a4e2d41655ea7214d61bf6ed34e1b.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61620a272dada8d4b9a9fab6379dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
您最近一年使用:0次
2019-02-06更新
|
2036次组卷
|
5卷引用:【市级联考】河南省驻马店市2018-2019学年高一上学期期末考试数学(理)试题
名校
6 . 已知圆C过点
,且与圆
外切于点
,
是x轴上的一个动点.
求圆C的标准方程;
当圆C上存在点Q,使
,求实数m的取值范围;
当
时,过P作直线PA,PB与圆C分别交于异于点P的点A,B两点,且
求证:直线AB恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79524ae8e494739dbcc5097a0f7c78a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45fb58388a2af941d6658d345829c198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fef9380b394a4bd829c83a5a5b4c859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50188630604c9019e00e79b21f32b20a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13364e4af8eb2ed915fa0f1caef47dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc304a55feec5d8312d3082f1bb91a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671e0271ef5d6f9784178b28d7d60265.png)
您最近一年使用:0次
2018-12-11更新
|
1293次组卷
|
3卷引用:【市级联考】江苏省苏州市常熟市2018-2019学年高二(上)期中数学试卷
【市级联考】江苏省苏州市常熟市2018-2019学年高二(上)期中数学试卷(已下线)第02练 圆与方程-2022年【寒假分层作业】高二数学(苏教版2019选择性必修第一册)河南省洛阳市洛宁县第一高级中学2022-2023学年高二上学期11月月考数学试题
7 . 已知圆的方程为
(1)求
的取值范围;
(2)若此圆与直线
相交于
两点,且
(
为坐标原点),求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a275cf1eaa67ae8d4723fb302a08d0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若此圆与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1cb41222d27da278a922db1cd5cb34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0287c9b8f2e10ddddc48caac86f48af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2018-11-19更新
|
660次组卷
|
2卷引用:【校级联考】安徽省宿州市十三所重点中学2018-2019学年高二上学期期中考试数学(理)试题
8 . 已知直线
与圆
相交于
两点,点
,且
,若
,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3016baf1a9ce777f16ea9ce469b2510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c62a5bc2ddd8b57ed3ab0e3adc507d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda168b06cad171bf06d1251897622b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada25f76504c3fd1226da43c94cb4277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dfb53b8cfebf749bf4c5d70a8b0cc7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2018-10-26更新
|
1934次组卷
|
2卷引用:【省级联考】四川省高2019届高三第一次诊断性测试(理科)数学
9 . 已知曲线
与圆
相交于
四个点,
,
在
轴右侧,
为坐标原点.
(1)当曲线
与圆
恰有两个公共点时,求
;
(2)当
面积最大时,求
;
(3)证明:直线
与直线
相交于定点
,求求出点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e982382b6150e6e6522ee3a3a64806f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/458fa9e9c5e308f8b8c8d90643e22560.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288c3d28135e0cde1209c8d475f45e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65436512ecbaefba4ac8123c55094211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)当曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e25b317906ca42ab1c73779cb462ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403d815e4db67e2d376951891c9e9813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)证明:直线
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
名校
10 . 已知过点A(0,4),且斜率为
的直线与圆C:
,相交于不同两点M、N.
(1)求实数
的取值范围;
(2)求证:
为定值;
(3)若O为坐标原点,问是否存在以MN为直径的圆恰过点O,若存在则求
的值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab821096dca880730ed3cadc2497a98.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c34414e65788c8605c35890188248c.png)
(3)若O为坐标原点,问是否存在以MN为直径的圆恰过点O,若存在则求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2018-12-02更新
|
1485次组卷
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5卷引用:【全国百强校】广东省汕头市金山中学2018-2019学年高二上学期期中考试 数学
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