1 . 如图,在平面直角坐标系
中,已知双曲线
的左顶点为
,右焦点为
,离心率为2,且经过点
,点
是双曲线右支上一动点,过三点
的圆的圆心为
,点
分别在
轴的两侧.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/a196c660-4b63-4844-968e-0c3abbd81265.png?resizew=195)
(1)求
的标准方程;
(2)求
的取值范围;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c40c376377e4a31da4dc4a007e976de6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ccfd5d01a4ca0cdb90cb9cdd3ad30d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9d525d0e30ee9983e77e667ba45323c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaa712e64750e3e2843bae68ebad6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/a196c660-4b63-4844-968e-0c3abbd81265.png?resizew=195)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae79c89e64da3de9ae6432e78c626f3.png)
您最近一年使用:0次
2 . 若实轴长为2的双曲线
上恰有4个不同的点
满足
,其中
,
,则双曲线C的虚轴长的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad29d7c31087e13e266793832af17bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de25799b89e589407065dae98d61d086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5a6ad215584ca01895369b13dadec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311497849126f1aaf1da0ec75602eabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b47e7bf02b3ca16f7d96b9369e51a3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-08-01更新
|
1412次组卷
|
7卷引用:安徽省皖西南联盟2018-2019学年高二下学期期末联考数学(理)试题