1 . 已知曲线C: ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15384f66e82a9e7a0405118f5e56766.png)
.
(1)求t为何值时,曲线C分别为椭圆、双曲线;
(2)求证:不论t为何值,曲线C有相同的焦点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15384f66e82a9e7a0405118f5e56766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2e350233894650267d35c790343dc2.png)
(1)求t为何值时,曲线C分别为椭圆、双曲线;
(2)求证:不论t为何值,曲线C有相同的焦点.
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21-22高二上·全国·课前预习
2 . 求满足下列条件的参数的值或取值范围.
(1)已知
,当
为何值时,①方程表示双曲线;②表示焦点在
轴上的双曲线;③表示焦点在
轴上的双曲线;
(2)已知双曲线方程为
,焦距为6,求
的值;
(3)椭圆
与双曲线
有相同的焦点,求
的值.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191fea45ff1f294a00e3b16e05778e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)已知双曲线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c611edeacddd8e9bde4198b86cd775e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996e27bd38f73ac37970225f09a9ee95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7e226a40cb115121ec380a5b06d703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
3 . 已知曲线
.
(1)当
时,求曲线C的焦点坐标(用a表示);
(2)当
时,讨论曲线C的类型.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3bf06d32748aabf1d9554d68b8c179c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1c36f271fe431eed0554d0a3394a47.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
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