名校
解题方法
1 . 如图,已知长方体
底面是边长为
的正方形,侧棱长为
,有一圆柱以平面
、平面
分别为上下底面,且其侧面与长方体除去平面
、平面
后剩余的四面均相切.点
为平面
截圆柱所得椭圆上的一动点.
![](https://img.xkw.com/dksih/QBM/2021/10/11/2826991532228608/2827553410154496/STEM/042d95c408ce4f2686508430902dd912.png?resizew=190)
(1)求平面
截圆柱所得椭圆的面积;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
![](https://img.xkw.com/dksih/QBM/2021/10/11/2826991532228608/2827553410154496/STEM/042d95c408ce4f2686508430902dd912.png?resizew=190)
(1)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3a8a0dfd7605db35891143f4bfc02f.png)
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