1 . 已知直线
与直线
相交于点
,且点
到点
的距离等于1,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6790fb30b961803dc860275b521573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58aa7e92a43011355af56a2dc538a8a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7374faef204b601022ace1f0a53c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() |
B.![]() |
C.![]() |
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3卷引用:湘豫名校联考2024届高三下学期第二次模拟考试数学试卷
名校
2 . 已知直线
,圆
,若直线
上存在两点
,圆
上存在点
,使得
,且
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f19aaade908e06a23641c11616b7336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb311a4f7daba572d3c976a77c1c3f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 已知圆
,圆
,过
上一点
作
的切线与
交于
不同两点,
,点
的坐标为
,则
的取值范围为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70feca8eac775ebee7b6d9760e2be6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af757ed187c61ded316b6894ff8a41e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384449e0100842eabd2142d1625467fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f9d08fccf0da8983522d37c2caa03e.png)
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4 . 已知圆
,圆
,若两圆相交,则实数
的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a95d4410057fc3f91d29562e389199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb59aa4b477b6d2b9934e6842be1303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-04-01更新
|
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3卷引用:上海市浦东新区2024届高三下学期期中教学质量检测数学试卷
上海市浦东新区2024届高三下学期期中教学质量检测数学试卷上海市吴淞中学2023-2024学年高二下学期第二次调研(5月)数学试卷(已下线)专题02 圆锥曲线--高二期末考点大串讲(沪教版2020选修)
5 . 直线
:
与
:
交于点P,圆C:
上有两动点A,B,且
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69efa05c9d7e9d7e8a435644b774744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f246d8cf62eacc904f01c0502558c43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95ab7ba0f4a1a78971163146eaa2ec5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529b4836786aca156de325464ea2ecd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3cc88a956e5e4805a1ebaf7a0e91ce.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:河南省济洛平许2024届高三第三次质量检测数学试题
解题方法
6 . 若圆
与圆
外切,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f696f360654d17c0b26f89bfbd76ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852f8adbd4f6938db6f80880f31b70ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd34eda66afc688494af1f8ca5704667.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 古希腊数学家阿波罗尼斯(约公元前262~公元前190年)的著作《圆锥曲线论》是古代数学的重要成果,其中有这样一个结论:平面内与两点距离的比为常数
的点的轨迹是圆,后人称这个圆为阿波罗尼斯圆,已知点
,
,动点
满足
,则点
的轨迹与圆
的公切线的条数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9731dae1942389db94dc06154015fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685d31faa9b3bc099e4c5a11b80088f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6bbbb53aaeab0ab7a242228cc510fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02944f857ad609ba773c81d5b5323c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c785e6ac28d06bb8c2e3863ba64ae6.png)
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3卷引用:湖南省长郡中学2023-2024学年高二下学期寒假检测(开学考试)数学试题
湖南省长郡中学2023-2024学年高二下学期寒假检测(开学考试)数学试题(已下线)专题3 阿波罗尼斯圆及其应用【练】(压轴小题大全)浙江省杭州市浙里特色联盟2023-2024学年高二下学期4月期中联考数学试题
2024高三下·全国·专题练习
8 . 求过两圆
和
的交点且面积最小的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a143573e9fe53e6a861154bf5b4c27c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dee1bfa7b7b2b6f730e5c926a9df570.png)
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9 . 一动圆圆E与圆
外切,同时与圆
内切.
(1)求动圆圆心E的轨迹方程;
(2)设A为E的右顶点,若直线
与x轴交于点M,与E相交于点B,C(点B在点M,C之间),若N为线段
上的点,且满足
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f518c9fc2dacbf894182827198b1ac09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a22d893a5ea8802c545df528d6278eba.png)
(1)求动圆圆心E的轨迹方程;
(2)设A为E的右顶点,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972c0a709b5da9da4241971c468dcb54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a81c7bff1585e43eb422287e0a8f258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff6689d2a34aba1b9215a83785d7b3a.png)
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10 . 已知点
在抛物线
上运动,过点
的两直线
与圆
相切,切点分别为
,当
取最小值时,直线
的方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/617d3975f2f3a55ebe30ec8001db6052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0873a0f3245544b4451ec5d2570dbe41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228bf1b66b2651cb40ec6912fc84b115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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