2021·浙江·模拟预测
1 . 如图,已知椭圆
与抛物线
,过椭圆下顶点
作直线
与抛物线交于
、
两点,且满足
,过点
作于直线
倾斜角互补的直线
交椭圆于
、
两点.
![](https://img.xkw.com/dksih/QBM/2021/5/21/2725927779696640/2725978904846336/STEM/576d9a48-75cc-4321-bc21-da714d467520.png?resizew=264)
(1)证明:点
的纵坐标为定值,并求出该定值;
(2)当
的面积最大时,求抛物线的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3cf706fe2ae0b2e99041ec1f4bf9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb65b40aec32d52c7d1a18702604210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2021/5/21/2725927779696640/2725978904846336/STEM/576d9a48-75cc-4321-bc21-da714d467520.png?resizew=264)
(1)证明:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
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2021-05-21更新
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4卷引用:广东省中山市中山纪念中学2023-2024学年高二下学期二月份综合测练(开学考)数学试卷