1 . 某地拟建造一座大型体育馆,其设计方案侧面的外轮廓如图所示,曲线
是以点
为圆心的圆的一部分,其中
;曲线
是抛物线
的一部分;
,且
恰好等于圆
的半径.假定拟建体育馆的高
(单位:米,下同).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/3db6c469-33cc-437b-93a0-637ea83bb392.png?resizew=156)
(1)若
,
,求
、
的长度;
(2)若要求体育馆侧面的最大宽度
不超过
米,求
的取值范围;
(3)若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074a95728962a5cf606dce0ccd1b52ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246518655504f9faaabcda467b8a9f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186c758f824939fc7de1be6b09506fc5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/3db6c469-33cc-437b-93a0-637ea83bb392.png?resizew=156)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843c9013e16ce26a4be297f1b61419fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7e0c8d8b6ac10b88aea344bf75a90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)若要求体育馆侧面的最大宽度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86608326541db75771f5de9db6187e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e469fee398e9ef371baf1b91cba2b0eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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2020-02-10更新
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3卷引用:专题13 三角恒等变换压轴题-【常考压轴题】