解题方法
1 . 已知双曲线
过点
,左右焦点分别为
,且
.
(1)求
的标准方程.
(2)设过点
的直线
与
交于
两点,问在
轴上是否存在定点
,使得
为常数?若存在,求出点
的坐标及该常数的值:若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50edfb9ed0d50d6f35ad6a130208d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682f50684ae25e45dfec0eaf8112a7a3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.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/d3a51949f48ee8cf746851ba779b078e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae88a1970c0af500b31bf366e30fff98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解题方法
2 . 已知椭圆
:
的左右焦点分别为
,
,
为椭圆
内一点.双曲线
:
经过点
和点
,则
①
的取值范围是________ ;
②若点
在椭圆
上,使得
,则
的离心率的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c6eca68147a28831ccb7a62b8a9d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e2ea7d8ddb2c73c32ab6d026f51328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8544f8483269db90305fa747eeac8b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d92f4c33e588fb66e316d9dfc559db.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce67e7428bbe1a3bbcd47da805a517b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
3 . 已知双曲线
的实轴长为4,且双曲线
经过点
.
(1)求双曲线
的标准方程;
(2)过点
且斜率不为零的直线
与双曲线
交于
两点,
关于
轴的对称点为
,求证:直线
过定点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b5a6870989fc9272e4d37f9d0b6304.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cc0f9aa168e43cc5759f017d69b498.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/fbdb21011ea821b91d539cb763aac649.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
4 . 已知双曲线
(
,
)的离心率为2,且经过点
.
(1)求双曲线
的方程;
(2)点
,
在双曲线
上,且
,
,
为垂足.证明:①直线
过定点;②存在定点
,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950e6108856cfb8d45b1a1e6aa6900e9.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59747cee312ee5140643428cae79efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7920d2550a6af7df3db60a33fe02c53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4110cc2b5dc3aabd585a8e9a81855a12.png)
您最近一年使用:0次
名校
解题方法
5 . 双曲线
(
,
)的离心率
,且过点
.
(1)求a,b的值;
(2)求与双曲线C有相同渐近线,且过点
的双曲线的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3851e0dbbf69218563787316dffcad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2e1166e08010dd2d91edcaca058c31.png)
(1)求a,b的值;
(2)求与双曲线C有相同渐近线,且过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a955cee9281eaead1a641eb9eec29a.png)
您最近一年使用:0次
2022-01-22更新
|
715次组卷
|
3卷引用:山东省烟台爱华高级中学2023-2024学年高二上学期期末模拟数学试题(一)B卷
6 . 如图,从某个角度观看篮球,可以得到一个对称的平面图形如下图,篮球的外轮廓为圆
,将篮球表面的粘合线视为坐标轴和双曲线,若坐标轴和双曲线与圆
的交点将圆的周长八等分,且
,则该双曲线的方程为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/6a11b3b0-1d23-4f8d-a7cd-bd9f85b9b2bc.png?resizew=273)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2d5a8b191148d64254f2bb1cd229af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/6a11b3b0-1d23-4f8d-a7cd-bd9f85b9b2bc.png?resizew=273)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-01-23更新
|
381次组卷
|
4卷引用:山东省烟台爱华高级中学2023-2024学年高二上学期期末模拟数学试题(二)B卷
名校
7 . 设经过点M(2,1)的等轴双曲线的左、右焦点分别为F1,F2,若此双曲线上的一点N满足
,则△NF1F2的面积为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9246af9a4775bbfb3bcf366e536fc6.png)
您最近一年使用:0次
2018-10-03更新
|
927次组卷
|
6卷引用:山东省青岛第十五中学2023-2024学年高二下学期期初质量检测试卷