在双曲线
中,把以原点为圆心、实轴长为直径的圆
叫做双曲线
的“伴随圆”,过双曲线
上任意一点
(顶点除外)作“伴随圆”
的两条切线,切点分别为
、
,若直线
在
、
轴上的截距分别为
、
,双曲线
的离心率为2,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316121fda44788cf7309270a426389e9.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316121fda44788cf7309270a426389e9.png)
更新时间:2024-05-26 10:58:34
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填空题-双空题
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解题方法
【推荐1】将单位圆
向右平移1个单位长度得圆E,过点
,
作圆E的切线
(斜率存在),切点坐标为
,则
=___________ ;设
),则数列
}的前2022项和为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e65e56a3c7f2c68fdd9c1c5f1ae401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7c5e7bd6bac51402ffa04b4144ec78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2415e7279e269ba133b7cdec84632964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0d5473737642c03eee4590688fc536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3bc8d58ebaa233c43bdf223a8f64e97.png)
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【推荐2】若
在圆
上运动,则
的最大值为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d46bb5ae37bd0665418641264409434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c2a60d020eca8e90d832b815489a3c.png)
您最近一年使用:0次
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名校
【推荐1】若双曲线
的渐近线与圆
相切,则该双曲线的实轴长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f262653a23ccc52b69a2adc1aa196853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1754846b9b36407340e6e69c381353c0.png)
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【推荐2】圆锥曲线具有优美的光学性质,如:光线从椭圆的一个焦点发出,被椭圆反射后会经过椭圆的另一个焦点.光线从双曲线的一个焦点发出,被双曲线反射后的反射光线等效于从另一个焦点射出.已知以坐标轴为渐近线的等轴双曲线
:
的图象以直线
为对称轴,从其中一个焦点发出的光线经双曲线反射后得到的反射光线与入射光线垂直,则入射光线与
的交点到中心的距离为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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填空题-单空题
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【推荐1】方程
表示的曲线即为函数
的图象,对于函数
,有如下结论:
①
在
上单调递减;
②函数
不存在零点;
③函数
的值域是
;
④
的图象不经过第一象限.
其中正确的命题是_______________________ .(填写命题序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e45f800ee73349ae154c1e303eb91b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2662cec2f06da6b3a405cb9ee6575152.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
其中正确的命题是
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【推荐2】在xOy平面上,将双曲线的一支![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58fa4a337f0b81b991fb32e8e6e3c0.png)
及其渐近线
和直线
、
围成的封闭图形记为D,如图中阴影部分,记D绕y轴旋转一周所得的几何体为
,过![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33639bac0f3423c147d8249d2b03ac9f.png)
作
的水平截面,计算截面面积,利用祖暅原理得出
体积为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58fa4a337f0b81b991fb32e8e6e3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab03556c333ab0b55fe86c937b2a5763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ac1756e6cc3266bd7198a024f871af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de72a5190834f5dbe895596656c038b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33639bac0f3423c147d8249d2b03ac9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420a53792e55c0f15b59dd617aa2140b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://img.xkw.com/dksih/QBM/2018/7/6/1982717610647552/1983425373126657/STEM/f357c694966549178d1d716e5aba0d12.png?resizew=158)
您最近一年使用:0次