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1 . (1)中心在原点,焦点在
轴上的双曲线W,经过点
,且其实轴长与椭圆
:
的焦距相等,求双曲线
的标准方程:
(2)已知A,B是椭圆
:
上两点,且A,B两点关于x轴对称,点A在第二象限,点
,
为等边三角形,求点
坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f4b244b3b0799cfb1994364036eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(2)已知A,B是椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f4b244b3b0799cfb1994364036eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a29ba49963134a7232fa8574105fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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解题方法
2 . 已知椭圆M与椭圆
有相同的焦点,且椭圆M过点
.点P在椭圆M上,
(1)求椭圆M的标准方程;
(2)设椭圆M的焦点为
,若
的面积为1,求点P的坐标.
(3)若
,
是椭圆M的左右顶点,点P与
,
不重合,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdf9283801878a6c22bf846afda22d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adee6fafc9dfb7126f0fb672518eb41.png)
(1)求椭圆M的标准方程;
(2)设椭圆M的焦点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10434ca8e058511b0dbcf652398f5b97.png)
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