名校
1 . 椭圆满足这样的光学性质:从椭圆的一个焦点发射光线,经椭圆反射后,反射光线经过椭圆的另一个焦点.如果没有阻挡,此过程可以不断重复进行下去.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/b0538397-e456-4c40-8ccc-67fdd26e1ad3.png?resizew=227)
(1)椭圆
,
分别为其左、右焦点.试问,从
发射的光线,经椭圆反射后第一次回到
时,光线经过的路程
的最大值和最小值分别为多少?(写出结论即可,无须说明)
(2)如图,椭圆
的左、右焦点分别为
,从
发射的光线,经椭圆上两点
处分别反射后,光线回到
,已知
,
,求椭圆
的离心率
的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/b0538397-e456-4c40-8ccc-67fdd26e1ad3.png?resizew=227)
(1)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6533a2123bcaa8c7dcd36d5e3f37700f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(2)如图,椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9cdcc25290844c9d4c088bf58afada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec24e02ffc2eeaeb0fdb41279ed4d497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f796f8a7de6ae278f2187e8917cd536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
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2 . 已知定圆
,点A是圆M所在平面内一定点,点P是圆M上的动点,若线段
的中垂线交直线
于点Q,则点Q的轨迹可能是:①椭圆;②双曲线;③抛物线;④圆;⑤直线;⑥一个点.其中所有可能的结果有( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90d9dd72446714e68f570da49b5445c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
A.3 | B.4 | C.5 | D.6 |
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3 . 已知定圆
:
,点
是圆
所在平面内一定点,点
是圆
上的动点,若线段
的中垂线交直线
于点
,则点
的轨迹可能是:①椭圆;②双曲线;③抛物线;④圆;⑤直线;⑥一个点.其中所有可能的结果有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a98a14a829938418bfff7745b9f13a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.2个 | B.3个 | C.4个 | D.5个 |
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2021-01-20更新
|
667次组卷
|
4卷引用:上海市复旦大学附属中学2020-2021学年高二上学期期末数学试题
上海市复旦大学附属中学2020-2021学年高二上学期期末数学试题(已下线)专题3.2 圆锥曲线【易错题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)四川省内江市资中县第二中学2020-2021学年高二下学期6月月考数学(理)试题四川省内江市资中县第二中学2020-2021学年高二下学期6月月考月考数学(文)试题
4 . 某市进行科技展览,其中有一个展品的一个截面由一条抛物线
和一个“开了孔”的椭圆
构成(小孔在椭圆的左上方).如图,椭圆与抛物线均关于x轴对称,且抛物线的顶点和椭圆的左顶点都在坐标原点,
为椭圆
的焦点,同时
也为抛物线
的焦点,其中椭圆的短轴长为
,在
处放置一个光源,其中一条光线经过椭圆两次反射后再次回到
经过的路程为8.由
处的光源照射的某些光线经椭圆反射后穿过小孔,再由抛物线反射之后不会被椭圆挡住.
(1)求抛物线
的标准方程;
(2)若由
处的光源发出的一条光线经由椭圆
上的点
反射后穿过小孔,再经抛物线上的点
反射后刚好与椭圆相切,求此时的线段
的长;
(3)在(2)的条件下,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/17/79773247-3bd2-499a-b682-ee3021db8569.png?resizew=129)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c30a7506331e47342fb1e7d2e12d041.png)
(3)在(2)的条件下,求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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