1 . 已知圆O:
,过点
的直线l交圆O于A,B两点,且
,则满足上述条件的一条直线l的方程为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318f2f6154dc3463b88fe889a5403c9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78b38b26298645002d65b5f239101db.png)
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2 . 已知
是椭圆
的左、右焦点,
是
上一点.过点
作直线
的垂线
,过点
作直线
的垂线
.若
的交点
在
上(
均在
轴上方
,且
,则
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a5b087c270dfc3f5ac18ebbc07edf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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3 . 设点
是曲线
上一点,则点
到直线
最小的距离为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec087e5a282a4bfa9fba07e456695c9.png)
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4 . 已知
,若平面内满足到直线
的距离为1的点
有且只有3个,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e18fd813ef878b9d7292620c757f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692265c4b64c721bd3e567b8af832b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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5 . 过圆
外一点
向圆O引两条切线
和
(其中A,B为切点),使得
,则实数a,b满足的等量关系为__________ ,
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827539d066d1b78e7ef8bc1569864971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b1c20fa9466374ae5ae611c76f62ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8115d5e4d5972c18fe5dd5752f107473.png)
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6 . 已知直线l与圆
相交于A,B两点,且弦的中点为
,若直线
与l垂直,则实数a的值是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345ce8cd12e7a9d0661f143bc2ddda46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03193aaea57bc6f935f2c299ecc2a238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a58518a9123df6b9ea048462c343a0c.png)
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7 . 若直线
与圆
:
有一个公共点,则实数
等于__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc0c80974cdebc2b1c645913288f583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf2581e33d804435aef88bdbc966d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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8 . “曼哈顿距离”是人脸识别中的一种重要测距方式,其定义如下:设
,
,则
,
两点间的曼哈顿距离
已知
,点
在圆
上运动,若点
满足
,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.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/79c04bbc507d8f917da5253fca7f2c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a5862f87bdbd8d6c653905cddb9900.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de86d9c0675d246a280f6b71a68aaf9d.png)
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9 . 双曲线
的左、右焦点分别是
,
,离心率为
,点
是
的右支上异于顶点的一点,过
作
的平分线的垂线,垂足是
,
,若
上一点
满足
,则
到
的两条渐近线距离之和为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9659f89dc162060c39417fee994c1bbb.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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10 . 已知抛物线
的焦点为
,直线
与抛物线
相切于点
(异于坐标原点
,与
轴交于点
,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
__________ ;向量
与
的夹角为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/c3904463e169fb25dbd36fa257edd2bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bad299e2782c072d27e1c54422cc8fc.png)
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