1 . 已知椭圆
,圆
(
为坐标原点).过点
且斜率为
的直线与圆
交于点
,与椭圆
的另一个交点的横坐标为
.
(1)求椭圆
的方程和圆
的方程;
(2)过圆
上的动点
作两条互相垂直的直线
,
,若直线
的斜率为
且
与椭圆
相切,试判断直线
与椭圆
的位置关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd432589cb00c29cac1806288e99ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63ab1f0053203fa5f310d191d0a987e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9903b063c08d9d3ada396cf598cc21.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)过圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcb166b53a49e393871bcb14a528792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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名校
2 . 在平面直角坐标系中,已知
的方程为
,平面内两定点
、
.当
的半径取最小值时:
(1)求出此时
的值,并写出
的标准方程;
(2)在
轴上是否存在异于点
的另外一个点
,使得对于
上任意一点
,总有
为定值?若存在,求出点
的坐标,若不存在,请说明你的理由;
(3)在第(2)问的条件下,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d59d7e0fc1f1f57b0c336f09eb5fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a62c9695f5a1691c5fe8724fa764b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2930d0f90e573deef7c80f9f0c446604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
(1)求出此时
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591ccce336af06e51e7f4887c287b80f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(3)在第(2)问的条件下,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352242e3bd9fc355639cc934bf60c921.png)
您最近一年使用:0次
2018-07-16更新
|
655次组卷
|
2卷引用:【全国百强校】黑龙江省大庆实验中学2017-2018学年高一下学期期末考试数学(理)试题
名校
3 . 在平面直角坐标系xOy中,已知圆心在
轴上的圆
经过两点
和
,直线
的方程为
.
(1)求圆
的方程;
(2)当
时,
为直线
上的定点,若圆
上存在唯一一点
满足
,求定点
的坐标;
(3)设点A,B为圆
上任意两个不同的点,若以AB为直径的圆与直线
都没有公共点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25ce60648ea5042ab5eb5702efe651a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfaaac9b7ed3db514f5bad049a23b389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3383a41791d728faf8dcaf0e509dda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)设点A,B为圆
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
4 . 已知点
,圆
.
(1)若点
在圆
内,求
的取值范围;
(2)若过点
的圆
的切线只有一条,求切线的方程;
(3)当
时,过点
的直线
被圆
截得的弦长为
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1de2c0218509a1f3ededd231f68894b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ab11ba6b230c4309e1b899eb58daae.png)
(1)若点
![](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/0a6936d370d6a238a608ca56f87198de.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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5 . 已知定点
在圆
的外部,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dab74e16403e8131f9f5b2a74f3a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abce3218e8541bda1981f4e84c1d8842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2020-08-13更新
|
370次组卷
|
3卷引用:人教A版(2019) 选择性必修第一册 过关斩将 第二章 直线和圆的方程 本章复习提升
人教A版(2019) 选择性必修第一册 过关斩将 第二章 直线和圆的方程 本章复习提升北师大版 必修2 过关斩将 第二章 解析几何初步 本章复习提升(已下线)第二章 直线和圆的方程 本章复习提升-2021-2022学年高二数学同步练习和分类专题教案(人教A版2019选择性必修第一册)
6 . 已知抛物线
.
(1)设
为抛物线
上横坐标为1的定点,
为圆
的一个动点,若
无公共点,且
的最小值为
,求
的值;
(2)已知
分别是抛物线的一条弦,且都不与
轴垂直,
与
相交于点
,
,若四边形
的四条边都存在斜率且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fbb6cbf601c8d08db363827baefc296.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6687210666a762b57d7df2679f7baebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105c883b9db4ff53c879b82f457b7f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c258c53a14590047273bf849d5713e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/f9829c6a040735f2965870076c784b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46893e2006c0abe95e2ad48e1455d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f5360aaef3df28eda2b2d267edabeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7496bc74d5f35d405b3debed173afb51.png)
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名校
7 . 已知椭圆
上的任意一点到它的两个焦点
,
的距离之和为
,且它的焦距为2.
(1)求椭圆C的方程;
(2)已知直线
与椭圆C交于不同的两点A,B,且线段AB的中点不在圆
内,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c92ae7a5cd7a0e337b758f0e443cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d241842f57772e0da3898fafa15e63f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆C的方程;
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe2d78f43611bad0d264eb3222f2472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55db71d9385e70266bd06330f261013b.png)
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解题方法
8 . 圆心在直线
上的圆C与y轴交于两点
,求圆C的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3275361febe6813d9efcee12334e9842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c89ebd106bf1e02cd0bfe7b6cba9ab.png)
您最近一年使用:0次
2020-09-14更新
|
319次组卷
|
3卷引用:湖南省长沙市雨花区2018-2019学年高一上学期期末数学试题
名校
9 . 如图,在平面直角坐标系
中,Q为第一象限内一点,
垂直于x轴,
垂直于射线
,垂足分别为A,B,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8143cb22eb8e56a83eecd1948e1554a9.png)
![](https://img.xkw.com/dksih/QBM/2020/8/8/2523555861856256/2524710068609024/STEM/967d162927bf42e1bf89479b0aaaeff5.png?resizew=182)
(1)求
的值;
(2)已知圆C通过O,A,Q,B四点
①求圆C的方程;
②设P是圆C上的任意一点,在x轴正半轴及射线
上是否分别存在定点E,F,使
为定值?若存在,指出定点的位置;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/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8143cb22eb8e56a83eecd1948e1554a9.png)
![](https://img.xkw.com/dksih/QBM/2020/8/8/2523555861856256/2524710068609024/STEM/967d162927bf42e1bf89479b0aaaeff5.png?resizew=182)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a84af713ec9898211637cfa1b0ef3b2.png)
(2)已知圆C通过O,A,Q,B四点
①求圆C的方程;
②设P是圆C上的任意一点,在x轴正半轴及射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4821eec9eb06107b9297db207544d62a.png)
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2020-08-10更新
|
325次组卷
|
2卷引用:江苏省南京市两校2019-2020学年高一下学期期末联考数学试题
名校
解题方法
10 . 如图,在平面直角坐标系中,点
,锐角
的终边与单位圆
交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/facb59ab-d066-4316-a2bf-5923729accc3.png?resizew=147)
(1)当
时,求
的值;
(2)若
,若点
在单位圆外,求
的取值范围;
(3)在
轴上是否存在定点
,使得对任意
,都有
恒成立?若存在,求出点
坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45516f9686130df59f8fb31b52b6b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/facb59ab-d066-4316-a2bf-5923729accc3.png?resizew=147)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4564e5162b6ba61483f2496f02bb35f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e0466bb18faf8983babb17a6fc13b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b94ef07d54f474823b72bc3f472749e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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