1 . 已知抛物线
的焦点与椭圆
的右焦点
重合,椭圆
的短轴长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/db796c73-9fe2-4363-a55d-fe74f5e68e21.png?resizew=151)
(1)求椭圆
的方程;
(2)过点
且斜率为
的直线
交椭圆
于
两点,交抛物线
于
两点,请问是否存在实常数
,使
为定值?若存在,求出
的值及定值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384a5ece40544f0dbe0ddd07400f5295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/db796c73-9fe2-4363-a55d-fe74f5e68e21.png?resizew=151)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8beef5e9a59a6e83f5cff1cd0ab70a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2022-11-18更新
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1235次组卷
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4卷引用:江苏省扬州市仪征中学2022-2023学年高二上学期期中数学试题