1 . 已知椭圆
的中心在坐标原点
,焦点在
轴上,左、右焦点分别为
、
,离心率
,短轴长为2,.
(1)求椭圆
的标准方程;
(2)设过
且斜率不为零的直线
与椭圆
交于
、
两点,过
作直线
的垂线,垂足为
,证明:直线
恒过一定点,并求出该定点的坐标;
(3)过点
作另一直线
,与椭圆分别交于
、
两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ea9f5967c96e60f03f332fd792cd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9d2abf13c2842f58654abf73c6b4ee.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e1ba8ef888dfe9a639dddd38d6d603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.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/17ae93479f71c86ffa37131326cfd993.png)
您最近一年使用:0次
2021-12-10更新
|
1117次组卷
|
3卷引用:2021年黑龙江省哈尔滨市第三中学校高二上学期期中数学试题
2021年黑龙江省哈尔滨市第三中学校高二上学期期中数学试题江西省赣州市赣县第三中学2021-2022学年高二12月月考数学(理)试题(已下线)易错点12 圆锥曲线-备战2022年高考数学考试易错题(新高考专用)
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2 . 已知椭圆
的一个顶点为抛物线
的焦点,点
在椭圆
上且
,
关于原点
的对称点为
,过
作
的垂线交椭圆于另一点
,连
交
轴于
.
(1)求椭圆
的方程;
(2)求证:
轴;
(3)记
的面积为
的面积为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6b146e6f1d0a3ca605c7cf26272228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088fcdd595455906a1a7080d630611f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b2da131e958f5a045dd3d5b0c68130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e4b0ddfa5aec71d6df83e574b56150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3a3db6d96518255f96ad7fc1ac98f4.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1addaf4de4d91f3553f7d0e5579fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ee2f999d11165c87e83c8862a35bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
2020-03-13更新
|
513次组卷
|
2卷引用:2019届黑龙江省学业水平考试数学(理科)试卷