已知F为双曲线
的左焦点,M,N为C上的点,点D(5,0)满足
,向量
的模等于实轴长的2倍,则△MNF的周长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de66df5b4cd1344339588b99bf7214a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eadda15b3b1298124318e2c3c8429d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7c19ffd67b5edd77b02d893f3c4156.png)
更新时间:2020-01-01 11:52:42
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【知识点】 利用定义解决双曲线中焦点三角形问题
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【推荐1】已知双曲线
的右焦点为
,点
在双曲线
上,且关于原点
对称.若
的面积为
,则双曲线
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acccb456555181c5dbef19a954ef6e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67336ccd79b321083fa8821e524c7467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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【推荐2】已知一簇双曲线
:
(
且
),设双曲线
的左、右焦点分别为
、
,
是双曲线
右支上一动点,
的内切圆
与
轴切于点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb09ecc6a5cb9c64a9a61abd6f7c48c4.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3804b43110c90af7678c43b35fc7c0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2aa78c96db411c9e1e939ae16de78d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d93a22c60e7efecc16849f7769563ef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628a2bd7f7b1040703c92c8443d8ec58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97bd958cf5841a89459dc3bcb8d8fda8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d226ec7d367a7f5b60293eee00f4f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9445875e1d2f78a79c38a04897435418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b25286f6029da66ce5270aacd05184f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb09ecc6a5cb9c64a9a61abd6f7c48c4.png)
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