名校
解题方法
1 . 在平面直角坐标系
中,已知椭圆
(
过点
,且离心率
.
(1)求椭圆C的方程;
(2)直线l的斜率为
,直线l与椭圆C交于A、B两点,求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4754fbe523ca63eba3810a3f88f37df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
(1)求椭圆C的方程;
(2)直线l的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
您最近一年使用:0次
2024-02-04更新
|
904次组卷
|
19卷引用:安徽省淮北市第一中学2018-2019学年高二下学期期中数学(文)试题
安徽省淮北市第一中学2018-2019学年高二下学期期中数学(文)试题安徽省淮北市相山区淮北师范大学附属实验中学2019-2020学年高二上学期期末数学(文)试题天津市津南区咸水沽第一中学2020-2021学年高二上学期期中数学试题(已下线)江苏省南通市如皋市2021-2022学年高二上学期期中数学试题天津市宁河区芦台第一中学2022-2023学年高二上学期期中考前统练数学试题宁夏石嘴山市第三中学2019-2020学年高二上学期第二次月考数学(文)试题山西大学附中2019-2020学年高二(12月份)第四次诊断数学(文科)试题(已下线)重难点5 解析几何-2021年高考数学【热点·重点·难点】专练(山东专用)(已下线)专题9.3 椭圆(精练)-2021年新高考数学一轮复习学与练广西田东县田东中学2020-2021学年高二上学期期末测试数学(理)试题天津市宁河区芦台第一中学2022-2023学年高二上学期11月月考数学试题广西玉林市博白县第四中学(博白县中学书香校区)2022-2023学年高二上学期12月段考数学试题海南省海口市海南中学2023-2024学年高二上学期期末数学模拟试题河南省洛阳市偃师高级中学2022-2023学年高一下学期4月月考数学试题重庆市渝高中学校2023-2024学年高二下学期阶段测试数学试题重庆市铜梁一中等重点中学2023-2024学年高二下学期3月月考数学试题湖北省武汉市第七中学2023-2024学年高二下学期3月月考数学试卷湖北省天门市天门中学2023-2024学年高二下学期3月月考数学试题(已下线)信息必刷卷01(北京专用)
名校
解题方法
2 . 在平面直角坐标系
中,已知椭圆
的离心率为
,且右焦点
到直线
的距离为
.
(2)设椭圆
上的任一点
,从原点
向圆
引两条切线,设两条切线的斜率分别为
,
(i)求证:
为定值;
(ii)当两条切线分别交椭圆于
时,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629bfcff97c1eb0873624fde373f3e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27567d43c5b91382ee3d7ca708ee422.png)
(2)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc56264b264eb7fcd697296ef415600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f767296276ab772cd8fb363916a37837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c445e365a6128937713669370d40c9.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
(ii)当两条切线分别交椭圆于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3da4a3cdea23c31f1b337571b9a4d9.png)
您最近一年使用:0次
名校
3 . 已知椭圆C:
(
)的离心率为
,点A,B分别是椭圆C的上,下顶点,且
.
(1)求椭圆C的标准方程;
(2)过点
且斜率为k的直线l交椭圆C于E,G两点,设直线AE与直线
交于点H,点H是否在直线BG上?若是,请证明之,若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699fc9b7e879af4866aaa07848dfb423.png)
(1)求椭圆C的标准方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bdfbae913ff7ff8caaefcaacf8c20ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
您最近一年使用:0次
名校
4 . 已知椭圆E:
的离心率为
,上、下顶点分别为A,B,右顶点为C,且
的面积为6.
(1)求E的方程;
(2)若点P为E上异于顶点的一点,直线是AP与BC交于点M,直线CP交y轴于点N,试判断直线MN是否过定点?若是,则求出该定点坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe2c533dbc23a34518f72f3cb14f330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)求E的方程;
(2)若点P为E上异于顶点的一点,直线是AP与BC交于点M,直线CP交y轴于点N,试判断直线MN是否过定点?若是,则求出该定点坐标;若不是,请说明理由.
您最近一年使用:0次
2023-11-19更新
|
451次组卷
|
4卷引用:安徽省芜湖市镜湖区安徽师大附中2023-2024学年高二上学期期中数学试题
解题方法
5 . 椭圆
的中心在坐标原点
,焦点在
轴上,离心率为
点
、
、
在椭圆
上,且
.
(1)求椭圆
的方程及直线
的斜率;
(2)当
时,证明原点
是
的重心,并求直线
的方程.
![](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/521e42b220eaac30bce6102bd8642104.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0dfb290b1a84f670549554a0c988593.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334355d1680c3a839900d3bc9fa8ce97.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc895959e9bc92294dc9dd2263dbf0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
6 . 已知椭圆
的左、右焦点分别为点
,短轴的上、下端点分别为
,若椭圆的离心率为
,四边形
的面积为
.
(1)求椭圆
的标准方程;
(2)设两条直线
与
交于椭圆的右焦点,且互相垂直,直线
交椭圆
于点
,直线
交椭圆
于点
,探究:是否存在这样的四边形
,使得其面积为
?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6939353e2387477b4149848a2818e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e89eeabfbd71ecce6f4c9a89ccb695e.png)
您最近一年使用:0次
2023-09-09更新
|
409次组卷
|
3卷引用:安徽省池州市第一中学等校2022-2023学年高二下学期期中联考数学试题
解题方法
7 . 设椭圆
过点
,离心率为
.
(1)求
的标准方程;
(2)若过点
且斜率为1的直线
与
交于
两点,求线段
中点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b515ff6809fe921bd2c8cadf198db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
解题方法
8 . 已知椭圆W:
的离心率为
,左、右焦点分别为
,
,过
且垂直于x轴的直线被椭圆W所截得的线段长为
.
(1)求椭圆W的方程;
(2)直线
与椭圆W交于A,B两点,连接
交椭圆W于点C,若
,求直线AC的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
(1)求椭圆W的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa841ce5d58b64f747a3c1b69bb20a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6950900f2551c9b195f16d617275adfe.png)
您最近一年使用:0次
2022-11-23更新
|
336次组卷
|
7卷引用:安徽省黄山市“八校联盟”2022-2023学年高二上学期11月期中考试数学试题
名校
9 . 已知椭圆C:
的右焦点为F,上顶点的坐标为
,离心率为
.
(1)求C的方程;
(2)设过F的直线l与C相交于点A,B两点,若
(O为坐标原点),求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe12fb284fc8e2502c9043be594c852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)求C的方程;
(2)设过F的直线l与C相交于点A,B两点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
您最近一年使用:0次
名校
解题方法
10 . 在平面直角坐标系中,椭圆
:
的离心率为
,焦距为
.
(1)求椭圆
的方程.
(2)若过椭圆
的左焦点,倾斜角为
的直线与椭圆交于
,
两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.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/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
2022-11-15更新
|
1635次组卷
|
6卷引用:安徽省马鞍山市第二中学2022-2023学年高二上学期期中数学试题