【定义】若抛物线与一水平直线交于两点,我们把这两点间线段的长称为抛物线关于这条直线的跨径,抛物线的顶点到该直线的距离称为抛物线关于这条直线的矢高,矢高与跨径的比值称为抛物线关于这条直线的矢跨比.如图1,抛物线
的顶点为
轴于点
,它与
轴交于点
,则
的长为抛物线
关于
轴的跨径,
的长为抛物线
关于
轴的矢高,
的值为抛物线
关于
轴的矢跨比.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/c533096f-1aef-4cbb-8dda-772cb98db470.png?resizew=544)
(1)【特例】如图2,已知抛物线
与
轴交于点
(点
在点
右侧)抛物线
关于
轴的矢高是______,跨径是______,矢跨比是______;
(2)【应用】如图3是某地一座三连拱桥梁建筑示意图,其中主跨与边跨的拱轴线为开口方向与大小一样的抛物线,它们关于水平钢梁所在直线的跨径分别为420米与280米,已知主跨的矢跨比为
,请求出边跨的矢跨比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa99bc7c5c2c05b67f84053a6871e612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129dac135251933324b0a0d0fefb5cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/c533096f-1aef-4cbb-8dda-772cb98db470.png?resizew=544)
(1)【特例】如图2,已知抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c147a4288bca20398a5162b38420bc4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c147a4288bca20398a5162b38420bc4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)【应用】如图3是某地一座三连拱桥梁建筑示意图,其中主跨与边跨的拱轴线为开口方向与大小一样的抛物线,它们关于水平钢梁所在直线的跨径分别为420米与280米,已知主跨的矢跨比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
更新时间:2023-12-14 22:38:43
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