名校
解题方法
1 . 已知椭圆
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
.圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
的圆心
在椭圆
上.点
到椭圆
的右焦点的距离为
.
![](https://img.xkw.com/dksih/QBM/2020/12/11/2611897288654848/2613455885336576/STEM/12aec4fd-f1f6-4611-86c4-e0e0a605122e.png?resizew=306)
(1)求椭圆
的方程;
(2)过点
作互相垂直的两条直线
,
,且
交椭圆
于
,
两点,直线
交圆
于
,
两点,且
为
的中点,求
的面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434249d6640b0c1a712d215cf8b83d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441f06d70c0e009e84d44f7d581d48d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df31c675af44a719b896de0f4bb163db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://img.xkw.com/dksih/QBM/2020/12/11/2611897288654848/2613455885336576/STEM/12aec4fd-f1f6-4611-86c4-e0e0a605122e.png?resizew=306)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
您最近一年使用:0次
2020-12-13更新
|
359次组卷
|
11卷引用:【全国百强校】黑龙江省大庆实验中学2017-2018学年高二下学期期中考试数学(文)试题
【全国百强校】黑龙江省大庆实验中学2017-2018学年高二下学期期中考试数学(文)试题黑龙江省哈尔滨市第九中学校2023-2024学年高二上学期12月月考数学试题2016届山西晋城市高三下学期三模考试理数学试卷2017届重庆市巴蜀中学高三上月考一数学(理)试卷江西省上高县第二中学2016-2017学年高二第七次月考(5月)数学(理)试题四川省成都市双流中学2018届高三上学期9月月考数学(文)试题(已下线)《2018届优生-百日闯关系列》数学专题三 第二关 以解析几何中与椭圆相关的综合问题【全国百强校】内蒙古杭锦后旗奋斗中学2018-2019学年高二上学期第二次(12月)月考数学(理)试题【全国百强校】江苏省如东高级中学2018-2019学年高二上学期第二次月考数学试题山东省济南市历城第二中学2019-2020学年高二上学期12月月考数学试卷辽宁省本溪市重点高中2020-2021学年高二12月月考数学试题
名校
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
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2卷引用:黑龙江省哈尔滨市第三中学2019-2020学年高二上学期期中数学(理)试题
名校
3 . 已知椭圆
上的点到焦点的最大距离为3,离心率为
.
(1)求椭圆
的标准方程;
(2)设直线
与椭圆
交于不同两点
,与
轴交于点
,且满足
,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c654f3bb56ece42d29a9f14cca37bf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c607b5b42a5a89320a014a50096bb36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ac93d47a037beec74d458ce7f53075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2019-01-18更新
|
503次组卷
|
4卷引用:黑龙江大庆实验中学2019-2020学年下学期实验三部期中考试高二数学理科试题
名校
4 . 椭圆
的左、右焦点分别为
,过
的直线
与椭圆交于
两点,若
的倾斜角为
时,
是等边三角形.
(1)求椭圆的方程;
(2)若
,求
中
边上中线长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f49644cd9fa4688cc3a74a234952530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42dfeedb1b7bf383520fd0853ff14f32.png)
(1)求椭圆的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c758c4afcd1e5656274b4af775fbc4a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635a0150fe965ced8935d7479b22c508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2018-05-03更新
|
743次组卷
|
2卷引用:黑龙江省大庆市大庆实验中学2019-2020学年高二上学期期中数学(文)试题
名校
5 . 已知椭圆
的两焦点与短轴的一个端点的连线构成等腰直角三角形,直线
与以椭圆C的右焦点为圆心,以椭圆的长半轴长为半径的圆相切.
(Ⅰ)求椭圆C的方程;
(Ⅱ)设P为椭圆C上一点,若过点
的直线
与椭圆C相交于不同的两点S和T,满足
(O为坐标原点),求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37dee169ffb6cbf86f5571ef6f42acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8a3365e99f926b1dafa901ab232152.png)
(Ⅰ)求椭圆C的方程;
(Ⅱ)设P为椭圆C上一点,若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a0d4c22734cac795de1e5c5fbefa87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bf404b2f0c501ae4859d4b6c2b3977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2016-12-03更新
|
1695次组卷
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12卷引用:黑龙江省哈尔滨市第九中学2019-2020学年高二上学期期中数学理试题
黑龙江省哈尔滨市第九中学2019-2020学年高二上学期期中数学理试题黑龙江省佳木斯市第一中学2021届高三第六次调研考试数学试卷(理科)2015届河南省商丘市高三第二次模拟考试理科数学试卷2015届河南省商丘市高三第二次模拟考试文科数学试卷2016届甘肃省兰州一中高三12月月考理科数学试卷2016届甘肃省兰州一中高三12月月考文科数学试卷2015-2016学年北大附中河南分校高二宏志班理科数学试卷2016届江西省赣中南五校高三下学期2月第一次联考理科数学试卷2016届江西省赣中南五校高三下学期2月第一次联考文科数学试卷2016届福建厦门双十中学高三下热身考理科数学试卷安徽省淮南市2018届高三第一次(2月)模拟考试数学(理)试题河南省南阳市华龙高级中学2020-2021学年上学期高三第二次月考文科数学试题