19-20高二·浙江·期末
解题方法
1 . 把椭圆
的短轴和焦点连线段中较长者、较短者分别作为椭圆
的长轴、短轴,使椭圆
变换成椭圆
,称之为椭圆的一次“压缩”.按上述定义把椭圆
“压缩”成椭圆
,得到一系列椭圆
,…当短轴长与焦距相等时终止“压缩”.经研究发现,某个椭圆
经过
次“压缩”后能终止,则椭圆
的离心率可能是①
,②
,③
,④
中的______ .(填写所有正确结论的序号)
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解题方法
2 . 如图,某同学用两根木条钉成十字架,制成一个椭圆仪.木条中间挖一道槽,在另一活动木条
的P处钻一个小孔,可以容纳笔尖,A,B各在一条槽内移动,可以放松移动以保证
与
的长度不变,当A,B各在一条槽内移动时,P处笔尖就画出一个椭圆E.已知
,且P在右顶点时,B恰好在
点,则E的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108a30042e37f9134f9f165c8415c0bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/6dcd181b-f70a-4a6f-8088-cd788b6c6294.png?resizew=190)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 如图,某同学用两根木条钉成十字架,制成一个椭圆仪.木条中间挖一道槽,在另一活动木条
的
处钻一个小孔,可以容纳笔尖,
各在一条槽内移动,可以放松移动以保证
与
的长度不变,当
各在一条槽内移动时,
处笔尖就画出一个椭圆
.已知
,且
在右顶点时,
恰好在
点,则
的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/5/c8320702-1e97-4658-967f-4eab2c28e36d.png?resizew=188)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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A.![]() | B.![]() | C.![]() | D.![]() |
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2023-05-04更新
|
1050次组卷
|
5卷引用:浙江省杭州市、宁波市部分学校2022-2023学年高三下学期4月联考数学试题
4 . 已知圆锥曲线
的方程为
.
(
)在所给坐标系中画出圆锥曲线
.
(
)圆锥曲线
的离心率
__________.
(
)如果顶点在原点的抛物线
与圆锥曲线
有一个公共焦点
,且过第一象限,则
(i)交点
的坐标为__________.
(ii)抛物线
的方程为__________.
(iii)在图中画出抛物线
的准线.
(
)已知矩形
各顶点都在圆锥曲线
上,则矩形
面积的最大值为__________.
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(
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(
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(
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(i)交点
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(ii)抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(iii)在图中画出抛物线
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(
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