名校
解题方法
1 . 如图,已知半圆C1:
与x轴交于A、B两点,与y轴交于E点,半椭圆C2:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc35409c8054fe18431c70e6fea0334.png)
的上焦点为F,并且
是面积为
的等边三角形,将由C1、C2构成的曲线,记为“Γ”.
(2)直线l:
与曲线Γ交于M、N两点,在曲线Γ上再取两点S、T(S、T分别在直线l两侧),使得这四个点形成的四边形MSNT的面积最大,求此最大面积;
(3)设点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7296bf80a4e4f4d1d7dfbfac932f501b.png)
,P是曲线Γ上任意一点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4d6974ef64ca22bfcc21b89f1acd26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc35409c8054fe18431c70e6fea0334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc1fd99348d416fa10a5aa050da2fbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(2)直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bdeeb6f5e38e3464c357d00839a6ce.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7296bf80a4e4f4d1d7dfbfac932f501b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe769c9fc76089fad3e748178fbaeb09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c687dd603610c9cd384ba2202e37e52.png)
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12卷引用:上海市进才中学2020-2021学年高二上学期期末数学试题
上海市进才中学2020-2021学年高二上学期期末数学试题(已下线)专题4.2 圆锥曲线【压轴题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)上海市复兴高级中学2020-2021学年高二下学期期中数学试题上海市七宝中学2021-2022学年高二下学期开学考数学试题上海市南汇中学2022-2023学年高二下学期期中数学试题(已下线)高二下期中真题精选(易错46题专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)专题02 圆锥曲线--高二期末考点大串讲(沪教版2020选修)重庆市第一中学校2023-2024学年高二上学期9月月考数学试题(已下线)第三章 圆锥曲线的方程(易错必刷30题9种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)广东省惠州市2024届高三上学期第三次调研考试数学试题广东省惠州市2024届高三上学期第三次调研考试数学试题(已下线)黄金卷07(2024新题型)
2 . 已知四棱锥
的底面ABCD是正方形,SA⊥底面ABCD,E是SC上的任意一点.
(2)设
,求点A到平面SBD的距离;
(3)当
的值为多少时,二面角
的大小为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfa640cf1e466119481efe1eb587863.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8d821ea1e4a2a099b4ec6b175db481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c53f1e79257ff52a0408fdc482488d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231b861d6d1f1d0b9f52b041cb40eb62.png)
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9卷引用:上海市实验学校2020-2021学年高二下学期期末数学试题
上海市实验学校2020-2021学年高二下学期期末数学试题四川省绵阳中学2022届高三上学期第一次质量检测数学试题(已下线)2021年秋季高三数学开学摸底考试卷02(新高考专用)(已下线)专题1.11 空间向量与立体几何大题专项训练(30道)-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)上海市彭浦中学2022-2023学年高二上学期期中数学试题(已下线)3.4 空间向量在立体几何中的应用(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020选修第一册)(已下线)核心考点05 空间向量及其应用(2)河北省石家庄市藁城区第一中学2020届高三下学期月考二数学(理)试题选择性必修第一册综合测试卷-2022-2023学年高二上学期数学人教B版(2019)
3 . 已知椭圆
,过动点
的直线
交
轴于点
,交椭圆于点
,
(点
在第一象限),且
是线段
的中点,过点
作
轴的垂线交椭圆于另一点
,延长
交椭圆于点
.点
在椭圆上.
![](https://img.xkw.com/dksih/QBM/2021/6/27/2751611170848768/2784057166553088/STEM/74833893-7f30-4681-a2d3-2de4a8b597fc.png)
(1)求椭圆的焦距;
(2)设直线
的斜率为
,直线
的斜率为
,证明:
为定值;
(3)求直线
倾斜角的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a032dd225bdd793172220c494c2054e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d224886bff118ce5971c74f252fdfbc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0750f4c9c674954dac4239549dd50a71.png)
![](https://img.xkw.com/dksih/QBM/2021/6/27/2751611170848768/2784057166553088/STEM/74833893-7f30-4681-a2d3-2de4a8b597fc.png)
(1)求椭圆的焦距;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ded6dbecb802a8a296e767c4b41ea4.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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4卷引用:上海市奉贤区2020-2021学年高二下学期期末数学试题
上海市奉贤区2020-2021学年高二下学期期末数学试题(已下线)2.2 椭圆(提高练)-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)(已下线)3.1.2(整合练)椭圆的简单几何性质-2021-2022学年高二数学考点同步解读与训练(人教A版2019选择性必修第一册)(已下线)专题08 《圆锥曲线与方程》中的解答题压轴题(2)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
4 . 已知椭圆
的右焦点为
,短轴长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/3ac976db-a912-46a6-8d40-42b2cfcce35d.png?resizew=153)
(1)求椭圆
的方程;
(2)设S为椭圆
的右顶点,过点F的直线
与
交于M、N两点(均异于S),直线
、
分别交直线
于U、V两点,证明:U、V两点的纵坐标之积为定值,并求出该定值;
(3)记以坐标原点为顶点、
为焦点的抛物线为
,如图,过点F的直线与
交于A、B两点,点C在
上,并使得
的重心G在x轴上,直线AC交x轴于点Q,且Q在F的右侧,设
、
的面积分别为
、
,是否存在锐角
,使得
成立?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28368d6b49ffac576679af0fb93f9d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/3ac976db-a912-46a6-8d40-42b2cfcce35d.png?resizew=153)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82a5421934348a612982ca099723b63.png)
(2)设S为椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82a5421934348a612982ca099723b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82a5421934348a612982ca099723b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e24465466f48ab87451ee917263ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77227d4d2b4a96829fd5ae1dd7cad688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
(3)记以坐标原点为顶点、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4455cb5ef8fa02f8740a01ea658ed7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4455cb5ef8fa02f8740a01ea658ed7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4455cb5ef8fa02f8740a01ea658ed7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7572ecc467c061ef71cf4486ec63ec3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ea53e1a6ae39dfaefbcd787a08b2ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b156d90a9a7a7c23d87a35b0cce4453.png)
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5卷引用:上海市宝山区2020-2021学年高二下学期期末数学试题
上海市宝山区2020-2021学年高二下学期期末数学试题(已下线)第3章 圆锥曲线与方程 单元综合检测(能力提升)(单元培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)3.3 抛物线(难点)(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)3.3 抛物线的几何性质-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) (已下线)第2章 圆锥曲线 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
5 . 如果一个多边形的所有顶点均在某个函数的图象上,那么称此多边形为该函数的内接多边形.设函数
,
,若四边形
为函数
的内接正方形,则此正方形的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5416e1a79e0c8a8fd9716b68e2c5354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d2d6440f49511ff58a2596c8233a32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801d2e00a8aa233a86c881a8c3f8b2b9.png)
A.15或7 | B.10或7 | C.10或17 | D.15或17 |
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6 . 已知直线
与椭圆
交于
、
两点,且
在直线
的上方(如图所示).
![](https://img.xkw.com/dksih/QBM/2021/6/21/2747823062622208/2782297250414592/STEM/ecaebca9-b970-48cb-b779-3fc6b831b172.png?resizew=308)
(1)求常数
的取值范围;
(2)若
的面积最大,求直线
的斜率的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10462edd0dbd28fc3908fe32726211a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f60eef6cf563ceb168e36025d023db5.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/5dba969413d0c05cfea8cae5b37a7c21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2021/6/21/2747823062622208/2782297250414592/STEM/ecaebca9-b970-48cb-b779-3fc6b831b172.png?resizew=308)
(1)求常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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4卷引用:上海市徐汇区2020-2021学年高二下学期期末数学试题
上海市徐汇区2020-2021学年高二下学期期末数学试题江西省南昌市豫章中学2022届高三入学调研(B)数学(文)试题安徽省合肥市长丰县正心高级中学2019-2020学年高二下学期6月月考文科数学试题(已下线)专题42 盘点圆锥曲线中的面积问题——备战2022年高考数学二轮复习常考点专题突破
7 . 阿基米德(公元前287年-公元前212年,古希腊)不仅是著名的哲学家、物理学家,也是著名的数学家.他曾利用“逼近法”得到椭圆的面积等于圆周率
乘以椭圆的长半轴长与短半轴长的乘积在直角坐标系
中,椭圆
的面积为
,两焦点与短轴的一个顶点构成等边三角形,过点
且斜率不为0的直线
与椭圆
交于不同的两点A,B.
(1)求椭圆
的标准方程;
(2)求
面积的最大值;
(3)设椭圆E的左、右顶点分别为P,Q,直线PA与直线
交于点
,试问B,Q,F三点是否共线?若共线,请证明;若不共线,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2f172ac16da76136cd2faa0fa26915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c9dcfd9f4c5298035870cb88a34169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(3)设椭圆E的左、右顶点分别为P,Q,直线PA与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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5卷引用:上海市虹口区2020-2021学年高二下学期期末数学试题
上海市虹口区2020-2021学年高二下学期期末数学试题(已下线)2.2 椭圆(提高练)-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)(已下线)3.1.1 (整合练)椭圆及其标准方程-2021-2022学年高二数学考点同步解读与训练(人教A版2019选择性必修第一册)(已下线)专题16 圆锥曲线焦点弦 微点2 圆锥曲线焦点弦三角形面积湖北省武汉市华中师大第一附中2023-2024学年高二上学期期末模拟数学试题
8 . 已知抛物线
∶![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
的焦点坐标为
.
(1)若直线
被抛物线
截得的弦长为
,求抛物线
的方程;
(2)设
为点
关于原点
的对称点,
为抛物线上任意一点,求
的取值范围;
(3)过焦点
作直线交抛物线于
、
两点,满足
,过
作抛物线准线的垂线,垂足记为
,准线交
轴于
点,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75de1947893e5c7a4d98d4458398fd6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02084e69bca97d818f7e84bf1955508.png)
(3)过焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/7b2171a7e806dc496b06bfe0a3a043e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55eb5dce55873a06d8c8f83d8448d1a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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9 . 设点
、
分别是椭圆C:
的左、右焦点,且
,点M、N是椭圆C上位于
轴上方的两点,且向量
与向量
平行.
(1)求椭圆C的方程;
(2)当
时,求
的面积;
(3)当
时,求直线
的方程.
![](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/36fcadd63cbad0c7b883e04507232ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba39e809fac8f3ccb81f5bc4a71bec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8c53921a9bbb356d2da12fde7e3526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58caa827baae837a041c9b05f31c46e.png)
(1)求椭圆C的方程;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67fd31a29214fa32bf0422b452a22416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bad3be8e3fdeda3a12251d3751715e1.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d8098e85e1d02fac617d1222fb8e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbdbe9a17a23c44cec8c7475c4dc1a9.png)
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10 . 已知椭圆
分别为其左、右焦点.
![](https://img.xkw.com/dksih/QBM/2021/7/7/2759280002670592/2766979694034944/STEM/079e637de03949218c1393b8e19ef59a.png?resizew=185)
(1)若T为椭圆上一点,
面积最大值为
,且此时
为等边三角形,求椭圆的方程;
(2)若椭圆焦距长为短轴长的
倍,点P的坐标为
,Q为椭圆上一点,当
最大时,求点Q的坐标;
(3)若A为椭圆
上除顶点外的任意一点,直线AO交椭圆于B,直线
交椭圆于C,直线
交椭圆于D,若
,求
.(用a、b代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7060bc06a286bd3a935ccdeb12cb1bf7.png)
![](https://img.xkw.com/dksih/QBM/2021/7/7/2759280002670592/2766979694034944/STEM/079e637de03949218c1393b8e19ef59a.png?resizew=185)
(1)若T为椭圆上一点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c820e30560907adc6ad54b2918011e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c820e30560907adc6ad54b2918011e8e.png)
(2)若椭圆焦距长为短轴长的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4a9aa5d69583f0c2099169fd39936a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d66bcfa301fb06aaabf43836771fc580.png)
(3)若A为椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f7c5f881ff81df4ab5279689004ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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