2024高二下·上海·专题练习
1 . 已知点
在圆
上运动,若对任意点
,在直线
上均存在两点
,
,使得
恒成立,则线段
长度的最小值是 ______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2 . 已知圆
和
,则圆
与圆
的所有公切线中斜率的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0231054e6c414c66ba8abde47ff06437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b922e7e108033018a4fc74985bc528.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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3 . 已知圆
和圆
,则两圆公共弦所在直线的方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e25b317906ca42ab1c73779cb462ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126f8914f06e2ee55d92d15c2ec34920.png)
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4 . 已知圆
,圆
,直线
分别与圆
和圆
切于
两点,则线段
的长度为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8605717a59e1c4ee42988cd495ed9634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3b283ee75ecbdc2ec6ce3bc822805ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2024-04-10更新
|
620次组卷
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2卷引用:2024年河南省普通高中毕业班高考适应性测试数学试题
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5 . 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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6 . 与圆
和圆
都相切的直线方程是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14109ca57e97620d776d7ca312b425b.png)
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2024-03-07更新
|
358次组卷
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2卷引用:江苏省镇江市2023-2024学年高三下学期期初考试数学试卷
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解题方法
7 . 若两圆
和
恰有三条公切线,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682a66debd2eb778a039100b4e7dbc49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05685eca8c01fec0a3fba7725dc0753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a36788f401bb4522f7e9970269ea5cb.png)
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8 . 已知圆
,圆
,直线
.若直线
与圆
交于
两点,与圆
交于
两点,
分别为
的中点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098658ddd8826dc6637297e1e6c7acdc.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf7d969ee6f3131219a0ae5d40e971e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd271f008e07631f71d7e146ae8d94b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f61de965b9d38982e5a75af2737e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764c199d659322854377a92fee97642d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098658ddd8826dc6637297e1e6c7acdc.png)
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2024-02-27更新
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1329次组卷
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4卷引用:黑龙江省哈尔滨市第三中学校2024届高三学年第一次模拟考试数学试卷
黑龙江省哈尔滨市第三中学校2024届高三学年第一次模拟考试数学试卷(已下线)第1讲:直线系与圆系的应用【讲】(已下线)2024年高考数学全真模拟卷07(新题型地区专用)四川省绵阳南山中学2024届高三下学期4月绵阳三诊热身考试文科数学试题
解题方法
9 . 写出圆
:
与圆
:
的一条公切线方程________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579d7b3a6cdcf8aafc7defe020e4aeb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0f75b4efd9909155c8c262ff40af3.png)
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10 . 圆
与
的位置关系为______ ;与圆
,
都内切的动圆圆心的轨迹方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f137a4a18b73e7286db82588ba2fd975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5093d0fbea77573dd366f6a8361bbc2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2024-02-06更新
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718次组卷
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5卷引用:河南省信阳市固始县2023-2024学年高二上学期期末考试数学试卷