1 . 已知椭圆
的离心率为
,且经过点
,
为椭圆C的左右焦点,
为平面内一个动点,其中
,记直线
与椭圆C在x轴上方的交点为
,直线
与椭圆C在x轴上方的交点为
.
(1)求椭圆C的标准方程;
(2)①若
,证明:
;
②若
,探究
之间关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accf35598ee054f1bf8b6584641d6d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2752e086b85f9fbb95010bf771072af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b170470d02c85c1be9a3faff5eca0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c30a7506331e47342fb1e7d2e12d041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16c755ab3fea6ca99b13193a5d7e485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
(1)求椭圆C的标准方程;
(2)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838d4d7fa68e89d2f57952c5eaa019d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b54c90e36facebeb720f3531a07a467.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363dcefb342c51d2af3cf3b7d0599944.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62fbe72587d27b3eeb48abe809320de7.png)
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2023-02-09更新
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4卷引用:新疆维吾尔自治区乌鲁木齐市第十二中学2024届高三下学期2月月考数学试题