名校
解题方法
1 . 已知椭圆
:
(
).
(1)若椭圆
的焦距为6,求
的值;
(2)设
,若椭圆
上两点M,N满足
,求点N横坐标取最大值时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6e9badea4fda62bdbfa1ae44107fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
(1)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22840186db0afc0e2b2e8915ce79b998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d5450b9ec0e906919efbb87e5a9e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2 . 已知双曲线T与椭圆
共焦点,且焦点到T的渐近线的距离为
.
(1)求双曲线T的渐近线方程;
(2)已知过点
的直线l与双曲线T交于P,Q两点,线段PQ的中点为E,设过E,F的圆的半径为r.证明:当圆心在x轴上时,
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b87c183a0f86870e61f8a4b6de9df97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求双曲线T的渐近线方程;
(2)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e19568e40858410ac82aadf39ce819d.png)
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名校
解题方法
3 . 已知椭圆
的离心率为
,且过点
.
(1)求椭圆
的标准方程与焦距;
(2)若直线
与椭圆
交于
两点,记线段AB的中点为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcadfe766e5ce650c693bb394fb7473d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48cba9e280d050c09d34be88b6660cb4.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2063f17a7bc83cb7fb33e78d67562c4.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
经过点
,焦距为
.
(1)求椭圆E的标准方程;
(2)若四边形
内接于椭圆E,对角线交于坐标原点O,且这两条对角线的斜率之积为
,求证:四边形
的任意一组邻边的倾斜角互补.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd40fadf77c01c856c9e5848c4215fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆E的标准方程;
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
5 . 求适合下列条件的椭圆的标准方程:
(1)经过点
,且与椭圆
有共同的焦点.
(2)以坐标轴为对称轴,并且经过两点
,
;
(1)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baecabc9ef53d7bb5650a2d8226231c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b747db7eaf469c6d1607e4b0d028299f.png)
(2)以坐标轴为对称轴,并且经过两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30fc12a328d2b452795c494e0a4b4b3c.png)
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6 . 已知抛物线
以椭圆
的右焦点为焦点
.
(1)求抛物线方程.
(2)过
作直线
与抛物线交于
,
两点,已知线段
的中点
横坐标3,求弦
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求抛物线方程.
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316699c45f1c088945d0cd3bb46eecfb.png)
您最近一年使用:0次
2020-11-26更新
|
1276次组卷
|
8卷引用:安徽省宿州市泗县第一中学2020-2021学年高二上学期第二次月考数学(文)试题
安徽省宿州市泗县第一中学2020-2021学年高二上学期第二次月考数学(文)试题江苏省泰州中学2020-2021学年高二上学期期中模拟检测数学试题江苏省盐城市伍佑中学2021-2022学年高二上学期期中数学试题(已下线)第3章 双曲线与抛物线的方程及性质(A卷·夯实基础)-2021-2022学年高二数学同步单元AB卷(苏教版2019选择性必修第一册)【学科网名师堂】四川省眉山市第一中学2021-2022学年高二上学期期中考试数学(理)试题河北省唐山市第十一中学2021-2022学年高二上学期12月月考数学试题黑龙江省齐齐哈尔市三立高级中学2022-2023学年高二上学期期中考试数学试题黑龙江省虎林市实验高级中学2021-2022学年高二上学期期末数学试题
7 . 已知椭圆
的左、右焦点分别为
,
,且
,
,
成等比数列.
是椭圆上一点,设该椭圆的离心率为
.
(Ⅰ)求
;
(Ⅱ)求证:
;
(Ⅲ)若点
不与椭圆顶点重合,作
轴于
,
的平分线交
轴于
,试求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6dc791ae552024ea0df7905bf190f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace7c9e3da8613175ca07c54c116127a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259c264ece6717883e866168c9e8e74d.png)
(Ⅲ)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3a3db6d96518255f96ad7fc1ac98f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432aae51854129e8c10f7c34c0c3a79f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e46c4fdeba0467b9dc6da78c15e884a.png)
您最近一年使用:0次
8 . 已知椭圆
过点
,焦距长
,过点
的直线
交椭圆
于
,
两点.
(1)求椭圆
的方程;
(2)已知点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981fe6f202c7a549a96230f49c11ab89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdebfa07f9b53d79d119cd3a1048e78a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b435274b2b7b1fe454bb223b5a59d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc86613c8ad7fb3c3984870bf33cfe43.png)
您最近一年使用:0次
9 . 已知椭圆
.过点(m,0)作圆
的切线l交椭圆G于A,B两点.
(I)求椭圆G的焦点坐标和离心率;
(II)将
表示为m的函数,并求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0748ec234ec293d31b395d0549016e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
(I)求椭圆G的焦点坐标和离心率;
(II)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05da40a2d7dab5d6a003906ca19d4749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05da40a2d7dab5d6a003906ca19d4749.png)
您最近一年使用:0次
2019-01-30更新
|
3249次组卷
|
13卷引用:安徽省滁州市定远县育才学校2019-2020学年高二下学期4月月考数学(文)试题
安徽省滁州市定远县育才学校2019-2020学年高二下学期4月月考数学(文)试题2011年普通高中招生考试北京市高考理科数学(已下线)2012届河北省冀州中学高三上学期期中理科数学试卷(已下线)2012届江苏省东海二中高三第三次学情调查数学试卷(已下线)2011-2012学年吉林省长春二中高二上学期期末考试理科数学(已下线)2011—2012学年天津市天津一中高二第一学期期末理科数学试卷2015-2016学年山东省枣庄三中高二上学情调查理科数学卷福建省莆田第九中学2017-2018学年高二上学期期中考试数学(理)试题山西省实验中学2020-2021学年高二上学期第三次月考数学(理)试题山西省实验中学2019届高三上学期第四次月考数学试题陕西省西安市长安区第一中学2020-2021学年高二上学期期中数学(文)试题人教B版(2019) 选修第一册 北京名校同步练习册 第二章 平面解析几何初步 2.5椭圆 2.5.2椭圆的几何性质(二)北京名校2023届高三一轮总复习 第7章 解析几何 7.12 直线与圆锥曲线的位置关系(2)
解题方法
10 . 已知抛物线
的焦点
与椭圆
的一个焦点重合,点
在抛物线上,过焦点
的直线
交抛物线于
两点.
(1)求抛物线
的方程以及
的值;
(2)记抛物线
的准线与
轴交于点
,若
,
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157f5ed9e3057193196d77b9c9be5ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54de4418592fc1ce570effcc01209ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c9bdf3a9ca69f4c2e8303f142f0776.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61f20a5abdb5deef164c7d633c2c8fce.png)
(2)记抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/536e6e6e0bf918af146bc292572ac5fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499a8eceb4949dd64589ba0f8585a8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次