名校
1 . 在平面直角坐标系
中,若正方形
边长为1,
点在原点,
、
分别在
轴和
轴上.
(1)若点
在线段
上运动,求
的取值范围;
(2)已圆
,问是否存在被圆
所截的直线
交圆于两点
,
且
.若存在,求出直线
,若不存在说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab158dd9e96abcae0f115f54fa66c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0032962eb1db58bd4e57b616dc90ff.png)
(2)已圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b93694d167f0c9efe3e802c2c211c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4590f6fa2844795660b072aa8b7af0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acc3b50b12699a4a9a4cc391b8f5bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
2 . 如图,圆
与
轴交于
、
两点,动直线
(
)与
轴、
轴分别交于点
、
,与圆交于
、
两点(点
纵坐标大于点
纵坐标).
,点
与点
重合,求点
的坐标;
(2)若
,
,求直线
将圆分成的劣弧与优弧之比;
(3)若
,设直线
、
的斜率分别为
、
,是否存在实数
使得
?若存在,求出
的值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24e616b5a35ff372c78c1472f156ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71812e0762c0aaffb51cfef66156567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71812e0762c0aaffb51cfef66156567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70dcb8f9fffd4ed2f8d1e131f6bbb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfbbc4d9fe71c8e1acd808e8e96d327c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
解题方法
3 . 已知直线
、
与曲线
分别相交于点
、
和
、
,我们将四边形
称为曲线
的内接四边形.
(1)若直线
和
将单位圆
分成长度相等的四段弧,求
的值;
(2)若直线
,
与圆
分别交于点
、
和
、
,求证:四边形
为正方形;
(3)求证:椭圆
的内接正方形有且只有一个,并求该内接正方形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b6247b1fd8f53318489696368d7587.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839fe3fc3c8f825b040fb01da9d76df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa941aa5d428f5d78ec3f281464f826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69c0979b1f101dcde663c38f52a09b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f86faa8cedab85e739ced46d705de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1afb06047f96fecf3315242963770e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78517f1ddb423a9f6ec8ea56fb8c547d.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)求证:椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962840f570c741cdec23a455ef126c51.png)
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4 . 在平面直角坐标系
中,已知直线
,点
,若直线
上存在点
,满足
,则实数
的取值范围是__________ .
![](https://img.xkw.com/dksih/QBM/2016/3/3/1572516730486784/1572516736212992/STEM/eab058e1aed1414c91dd03d3b9950f61.png?resizew=28)
![](https://img.xkw.com/dksih/QBM/2016/3/3/1572516730486784/1572516736212992/STEM/979999b9d69a471fba3740a4a132e8dc.png?resizew=107)
![](https://img.xkw.com/dksih/QBM/2016/3/3/1572516730486784/1572516736212992/STEM/384bff79c37b49bfae9d0647fdc67c16.png?resizew=47)
![](https://img.xkw.com/dksih/QBM/2016/3/3/1572516730486784/1572516736212992/STEM/010446fdc70347748e155dfe81015d05.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2016/3/3/1572516730486784/1572516736212992/STEM/aad508aad8f342f293e4ae4c5e0d44bb.png?resizew=21)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6893b770d20cb65f909364d7c161d0.png)
![](https://img.xkw.com/dksih/QBM/2016/3/3/1572516730486784/1572516736212992/STEM/7f2426206699417c8516899b82fde8ab.png?resizew=13)
您最近一年使用:0次