1 . 【江苏省苏锡常镇四市2017-2018学年度高三教学情况调研(二)数学试题】如图,椭圆
的离心率为
,焦点到相应准线的距离为1,点
分别为椭圆的左顶点、右顶点和上顶点,过点
的直线
交椭圆于点
,交
轴于点
,直线
与直线
交于点
.
![](https://img.xkw.com/dksih/QBM/2018/7/25/1996163991904256/1997388793798656/STEM/f800325b8454471fb6d7b7278d7ba197.png?resizew=260)
(1)求椭圆的标准方程;
(2)若
,求直线
的方程;
(3)求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78c38805c09dcfbcc42103308975a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b378a2df371f5ff1815c03a84f571229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e04b713af80edc1be811c83e6c4fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345632b25ab00040c8930d20e20b9ad2.png)
![](https://img.xkw.com/dksih/QBM/2018/7/25/1996163991904256/1997388793798656/STEM/f800325b8454471fb6d7b7278d7ba197.png?resizew=260)
(1)求椭圆的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7806f1efe16b5e00b41ea74f7be1da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c60bb69220eb1f216bffa96dff09355.png)
您最近一年使用:0次
2011·江苏南京·一模
解题方法
2 . 在直角坐标系
中,直线
与
轴正半轴和
轴正半轴分别相交于
两点,
的内切圆为圆
.
(1)如果圆
的半径为1,
与圆
切于点
,求直线
的方程;
(2)如果圆
的半径为1,证明:当
的面积、周长最小时,此时
为同一个三角形;
(3)如果
的方程为
,
为圆
上任一点,求
的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)如果圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f119f6a7eabd36fca6ef25135311e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)如果圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502bea604848f203c3c6e33bb14318d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e0a0ceab1e6b30513ab7d0b5c376da.png)
您最近一年使用:0次
3 . 已知点
,
分别为线段
上的动点,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
(1)若
求直线
的方程;
(2)证明:
的外接圆恒过定点(异于原点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e91aee78b2293d162e117a7a15655a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c483745c2455e26d7e695f5727600ee8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a090d241903d3f409644768e5127568e.png)
您最近一年使用:0次
2016-12-03更新
|
1040次组卷
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8卷引用:2015届江苏省连云港、徐州、淮安、宿迁四市高三一模考试理科数学试卷