名校
1 . 已知圆
,圆
,点M,N分别是圆
、圆
上的动点,点
为
上的动点,则
的最小值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbba972744f3dddcc54cb5ef64cb2ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc5a717ed97272a4a56e10c589f3e86.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f618c20607afa7c345e81d33878148.png)
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名校
解题方法
2 . 点
关于直线
的对称点在圆
内,则实数
可以为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d8c32876b176d8539404ac4e02d085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79af8705af8a97bc8b02181377c658c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc216ef5fdef3b5b0803a0425f53679c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.4 | B.6 | C.8 | D.10 |
您最近一年使用:0次
名校
3 . 与直线
关于
轴对称的直线的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c5a26de743693d824f53cb1bc11227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
您最近一年使用:0次
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解题方法
4 . 已知
是抛物线
上一点,圆
关于直线
对称的圆为
,
是圆
上的一点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223cf57be5499bab6d7bf063f1ef1dbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1f76d593f96f17a696ce7634ab5bf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 光线从点
射到
轴上,经
轴反射后经过圆
上的点
,则该光线从点A到点
的路线长的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8c934a5b1e5481440d8de919a3771c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0749142e1d5c8f5b3fb8996643559af7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.9 | B.10 | C.11 | D.12 |
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名校
解题方法
6 . 唐代诗人李颀的诗《古从军行》开头两句:“白日登山望烽火,黄昏饮马傍交河”隐藏着一个有趣的数学问题——“将军饮马”,即某将军观望完烽火台之后从山脚的某处出发,先去河边饮马,再返回军营,怎样走能使总路程最短?在平面直角坐标系中有两条河流m,n,其方程分别为
,
,将军的出发点是点
,军营所在位置为
,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f7fbfa2214ca72495a993b2fed8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debb915eafbf76a3aed841bbf651a21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5548cf6f14c42364e7a6e9562ee5f88.png)
A.若将军先去河流m饮马,再返回军营,则将军在河边饮马的地点的坐标为![]() |
B.将军先去河流n饮马,再返回军营的最短路程是![]() |
C.将军先去河流m饮马,再去河流n饮马,最后返回军营的最短路程是![]() |
D.将军先去河流n饮马,再去河流m饮马,最后返回军营的最短路程是![]() |
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解题方法
7 . 已知椭圆
的左焦点为
,若
关于直线
的对称点
恰好在
上,且直线
与
的另一个交点为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c681798734b618e5ca129d2a9837d797.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](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/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c681798734b618e5ca129d2a9837d797.png)
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8 . 已知直线
,圆
.
(1)求直线
与圆
相交所得的弦长;
(2)求圆
关于直线
对称所得的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c0e2a689154e5eb5cd144fec96a809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a160c78f124d6ed7f2d2fb62d0d524.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
9 . 已知以点
为圆心的圆经过原点
,且与
轴交于点
,与
轴交于点
.
(1)求证:
的面积为定值.
(2)设直线
与圆
交于点
,
,若
,求圆
的方程.
(3)在(2)的条件下,设
,
分别是直线
和圆
上的动点,求
的最小值及此时点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f4b7f273d813a17f6a3a0a5592cd2af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056e249d0c33ef92b956f84937fa9324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab760f42892e987055c09495bd014554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4958a3ab5b7a862f715b14822710b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01881ba4fd330f2d1c95374c89b50ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024高三·全国·专题练习
解题方法
10 . 已知在
中,
,
.
(1)若
的面积为
,求点C的轨迹方程;
(2)若直线
平分内角C,求点C的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131ebfee8d3fd5d0c4d3b20012e232f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f3aec1dc12dc085258842c804e597b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d585d2d6643471640905d234d9538c5.png)
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