名校
解题方法
1 . 已知双曲线
,直线
为其中一条渐近线,
为双曲线的右顶点,过
作
轴的垂线,交
于点
,再过
作
轴的垂线交双曲线右支于点
,重复刚才的操作得到
,记
.
(1)求
的通项公式;
(2)过
作双曲线的切线分别交双曲线两条渐近线于
,记
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be56ac444cd8deb01180432555c86b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b293b8d25590ef6f6ae0e9e7486a32a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2214909d55698044e2d16019d902a79.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac2b5502151b6c1e7e3ffe3b8c8988fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7987d2fc837254192070e6a979aa00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32abe6c3ae6253b064f5e68c2a52bfb.png)
您最近一年使用:0次
2024-02-06更新
|
698次组卷
|
2卷引用:浙江省舟山市2023-2024学年高二上学期期末检测数学试题
名校
解题方法
2 . 已知点
为双曲线
上的动点.
(1)判断直线
与双曲线的公共点个数,并说明理由;
(2)(i)如果把(1)的结论推广到一般双曲线,你能得到什么相应的结论?请写出你的结论,不必证明;
(ii)将双曲线
的两条渐近线称为“退化的双曲线”,其方程为
,请利用该方程证明如下命题:若
为双曲线
上一点,直线
:
与
的两条渐近线分别交于点
,则
为线段
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea74737939c0f94c91229a7098f36ec.png)
(1)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e314fafd906934931d5cdfb4ecad2fca.png)
(2)(i)如果把(1)的结论推广到一般双曲线,你能得到什么相应的结论?请写出你的结论,不必证明;
(ii)将双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e56464f202655f76b90e0f89e91be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09cad114964b344e7c9b3903a21354e4.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/006d86d8f686ca9afaa3ef23a519728a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f5f4ad0caac5a0fecb64f3908d2290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2024-03-04更新
|
1262次组卷
|
5卷引用:广东省汕头市2024届高三第一次模拟考试数学试题
广东省汕头市2024届高三第一次模拟考试数学试题江苏省盐城市五校联考2023-2024学年高二下学期第一次学情调研检测(3月)数学试题山东省烟台市牟平第一中学2023-2024学年高二下学期3月限时练(月考)数学试题(已下线)第26题 圆锥曲线压轴大题(1)(高三二轮每日一题)(已下线)大招4 圆锥曲线创新问题的速破策略
解题方法
3 . 已知双曲线
为其左右焦点,点
为其右支上一点,在
处作双曲线的切线
.
(1)若
的坐标为
,求证:
为
的角平分线;
(2)过
分别作
的平行线
,其中
交双曲线于
两点,
交双曲线于
两点,求
和
的面积之积
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc23491d7056318109f283c04f7502fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460e1f707e43e4d7a8a2eb6bfaa435e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6114947179bed8c2c86ac078e2f8497f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c727ebc70e4c4060d2d163e01432fcff.png)
您最近一年使用:0次
2023-05-18更新
|
1665次组卷
|
8卷引用:第八章 平面解析几何(测试)
(已下线)第八章 平面解析几何(测试)(已下线)专题11 平面解析几何-4(已下线)专题06 圆锥曲线大题(已下线)专题8.3 双曲线综合【九大题型】(举一反三)(新高考专用)-2浙江省名校新高考研究联盟Z20联盟2023届高三第三次联考(三模)数学试题江苏省连云港市灌南高级中学2022-2023学年高二下学期第二次月考数学试题(已下线)第八章 解析几何 专题4 解析几何中的面积问题(已下线)考点20 常用的二级结论的应用 2024届高考数学考点总动员