1 . 以下四个关于圆锥曲线的命题中:
①设
、
为两个定点,
为非零常数,
,则动点
的轨迹为双曲线;
②过定圆
上一定点
作圆的动弦
,
为坐标原点,若
则动点
的轨迹为椭圆;
③方程
的两根可分别作为椭圆和双曲线的离心率;
④双曲线
有相同的焦点.
其中真命题的序号为________ .(写出所有真命题的序号)
①设
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/e41105eb63b149e49b30d6ac962c08a3.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/5d3820140060404c90332e226ca0cfe1.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/0b89f655331a44b58f650fea035be439.png?resizew=13)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db429aa080d7c56eeac7a83f5ea7eb1f.png)
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/ba10ed8a3a0b4fb3bf8dfe2febf9af44.png?resizew=16)
②过定圆
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/d23aa30797604e9cb6bb077bfecedd17.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/e41105eb63b149e49b30d6ac962c08a3.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/a64346ff9b50464c8cadd79b3553c7fa.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/0125600dc0ac48f19e3876b0e6318c3d.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18c0d52f7a06e016a827c8639b76cd3.png)
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/ba10ed8a3a0b4fb3bf8dfe2febf9af44.png?resizew=16)
③方程
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/fedf1ab1fecf4670ae200c37fe341395.png?resizew=108)
④双曲线
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668241408/STEM/d564972a103e4d7cb294f9296e67f20c.png?resizew=203)
其中真命题的序号为
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10-11高二下·江西上饶·阶段练习
2 . 在平面直角坐标系
中,双曲线
的离心率为
,求该双曲线的焦距.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0454a4e1f14d5e42c197d8c6d3313377.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
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