如图,一个酒杯的内壁的轴截面是抛物线的一部分,杯口宽
,杯深
,称为抛物线酒杯.
①在杯口放一个半径为
的玻璃球,则球面上的点到杯底的最小距离为________
;
②在杯内放入一个小的玻璃球,要使球触及酒杯底部,则玻璃球的半径的取值范围为________ (单位:
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095ab4a92bf822e175d370e6d0c8a730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b1fe1b971b780e443a9b13621611c5.png)
①在杯口放一个半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095ab4a92bf822e175d370e6d0c8a730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
②在杯内放入一个小的玻璃球,要使球触及酒杯底部,则玻璃球的半径的取值范围为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://img.xkw.com/dksih/QBM/2021/11/11/2849020654641152/2851113712066560/STEM/4a73d015-f3a7-4215-ac34-e79dd519c53b.png?resizew=262)
更新时间:2021-11-14 14:28:36
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【推荐1】如图是抛物线形拱桥,当水面在
时,拱顶离水面2米,水面宽4米,水位下降1米后,水面宽 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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【推荐2】我们知道:用平行于圆锥母线的平面(不过顶点)截圆锥,则平面与圆锥侧面的交线是抛物线一部分,如图,在底面半径和高均为2的圆锥中,
、
是底面圆
的两条互相垂直的直径,
是母线
的中点,已知过
与
的平面与圆锥侧面的交线是以
为顶点的圆锥曲线的一部分,则该圆锥曲线的焦点到其准线的距离等于__________ .
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【推荐1】过抛物线
上任意一点
作
轴的垂线,垂足为
,动点
在直线
上,则
的最小值为__________ .
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59739d25b10505248310e4be44ac44f4.png)
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【推荐2】设抛物线
的焦点为F,直线l过F且与抛物线交于P,Q两点.若
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f1303e1fb8f5787a084bd26a3d6729.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2c31287f28266e4bbee8390da832e2.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f1303e1fb8f5787a084bd26a3d6729.png)
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