1 . 已知抛物线
与圆
交于
两点,且
,直线
过
的焦点
,且与
交于
两点,给出下列命题:
①若直线
的斜率为
,则
;
②
的最小值为
;
③若以
为直径的圆与
轴的公共点为
,则点
的横坐标为
;
④若点
,则
周长的最小值为
.
其中真命题的序号为__________ (把所有正确命题的序号都填在横线上).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f62686f6f9118291c444a8d5a4d0f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9602114f45bdcb304e02710ae7bc0e08.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfcb3265d1351dc28c72f43e00f703e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755d7e08b98c26303f2f61de7e7ddd2.png)
③若以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1689fe3683efa40a48684bb229c1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
④若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba9f9108cac55a7758ec9f0a95c0805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcea00eeff85afba49364c1998ff4f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251ad4474e7322ac72981d9c423fd443.png)
其中真命题的序号为
您最近一年使用:0次
名校
解题方法
2 . 已知圆
与圆
,在下列说法中:
①对于任意的
,圆
与圆
始终相切;
②对于任意的
,圆
与圆
始终有四条公切线;
③
时,圆
被直线
截得的弦长为
;
④
分别为圆
与圆
上的动点,则
的最大值为4
其中正确命题的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f1dc81fb995b3023d56f82ff964a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a2314d1f465b9940f08e0b5f55f88a.png)
①对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe211e0dea7a44863e5e1706633c3aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a52e26180930ad5b56a8a45f28a0f2.png)
②对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe211e0dea7a44863e5e1706633c3aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a52e26180930ad5b56a8a45f28a0f2.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee117579f5fc3944bbf7f342f50e450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/601d4c79cdabd1a49a6b8e6d026e663f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef812f839622326a7d7027cc806aaeb.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b09e2d46f94b9ca3caf3f8283619c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a52e26180930ad5b56a8a45f28a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2a0f156c21a6d3387e9c5a15b373d1.png)
其中正确命题的序号为
您最近一年使用:0次
2022-10-13更新
|
974次组卷
|
8卷引用:四川省成都七中2019-2020学年高一下学期6月考试数学试题
2010·黑龙江哈尔滨·一模
解题方法
3 . 已知圆
与圆
,在下列说法中:
①对于任意的
,圆
与圆
始终相切;
②对于任意的
,圆
与圆
始终有四条公切线;
③当
时,圆
被直线
截得的弦长为
;
④
分别为圆
与圆
上的动点,则
的最大值为4.
其中正确命题的序号为______ .
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/931d726a0d4841ae9b1c03168c628d0a.png?resizew=220)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/5635d69a619847ba9aaf57794e9012c0.png?resizew=91)
①对于任意的
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/8369f20c30374e03a6b13f5d8f948a15.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/da9f02d104994c8485f6d4b5cd086f65.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/bdbc8b7398634450a3ff71a521b58b72.png?resizew=20)
②对于任意的
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/8369f20c30374e03a6b13f5d8f948a15.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/da9f02d104994c8485f6d4b5cd086f65.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/bdbc8b7398634450a3ff71a521b58b72.png?resizew=20)
③当
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/508345b0c6764b6d9d64ccd1991cf101.png?resizew=40)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/da9f02d104994c8485f6d4b5cd086f65.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/f15d3415524749a3ad5ff841d4133fd6.png?resizew=105)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/d6b1859244b4448a8674dc717d67ed9a.png?resizew=23)
④
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/02dccdc836cd4166996e9f20863e52e3.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/da9f02d104994c8485f6d4b5cd086f65.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/bdbc8b7398634450a3ff71a521b58b72.png?resizew=20)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1576715455873024/1576715601297408/STEM/67ece29fd5b54627952aefe0fdad7421.png?resizew=35)
其中正确命题的序号为
您最近一年使用:0次
名校
解题方法
4 . 经过坐标原点
且互相垂直的两条直线
和
与圆
相交于
四点,有下列结论:
①弦
长度的最小值为
;
②线段
长度的最大值为
;
③四边形
面积的取值范围为
.
其中所有正确结论的序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.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/02739371fabe090f3686cb8ec4046c12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6dec3ef34312fabcb98921ca46e60f.png)
①弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c19a9e99072c37a49b4eb21ae61bef.png)
②线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc098576babe079734625742950fe5a.png)
③四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01ec13e456c3fd5cb349edef516efeb.png)
其中所有正确结论的序号为
您最近一年使用:0次