名校
解题方法
1 . 已知椭圆
的左,右顶点分别为
,上顶点M与左,右顶点连线
的斜率乘积为
,焦距为
.
(1)求椭圆
的方程;
(2)设过点
的直线
与椭圆C交于
两点,O为坐标原点,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03df57efff473b3cfeb8503796b7d6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c6ba69264c8f203cd756581bc6280a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ff9f648fedec284a11a9761cb6183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-02-17更新
|
279次组卷
|
2卷引用:天津市瑞景中学2023-2024学年高二上学期期中考试数学试卷
名校
解题方法
2 . 设椭圆
的离心率
,过点
.
(1)求椭圆
的方程;
(2)求椭圆
被直线
截得的弦长.
(3)直线
与椭圆交于
两点,当
时,求
值.(O为坐标原点)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e90064d012356de1877aa697cd6d6ac.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-11-23更新
|
2945次组卷
|
4卷引用:天津市滨海新区塘沽第十三中学2022-2023学年高二上学期期中数学试题
天津市滨海新区塘沽第十三中学2022-2023学年高二上学期期中数学试题天津市滨海新区田家炳中学2023-2024学年高三上学期期中考试数学试题(已下线)上海市华东师范大学第二附属中学2022-2023学年高二下学期期末数学试题广东省东莞实验中学2022-2023学年高二下学期月考一数学试题
名校
解题方法
3 . 已知椭圆
:
的左右焦点分别为
,上顶点为
,长轴长为
,若
为正三角形.
(1)求椭圆
的标准方程;
(2)过点
,斜率为
的直线与椭圆相交
两点,求
的长;
(3)过点
的直线与椭圆相交于
两点,
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ac00c0db17b7bf34f758f73cd4c6a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-11-10更新
|
1481次组卷
|
5卷引用:天津市五校2022-2023学年高二上学期期中联考数学试题
名校
解题方法
4 . 已知椭圆
,直线l过点
与椭圆Γ交于A,B两点,O为坐标原点.
(1)设C为线段AB的中点,当直线l的斜率为
时,求线段OC的长;
(2)当直线l的斜率为
时,求三角形AOB的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7b1b8a84ae7a1b2243b78cc932860d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa71aa2ea224669698850108751a71a.png)
(1)设C为线段AB的中点,当直线l的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(2)当直线l的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047616f1d1d39bf6c3cd07cf63ef5b80.png)
您最近一年使用:0次
名校
解题方法
5 . 已知椭圆
的离心率为
,直线
被椭圆C截得的线段长为
.
(1)求椭圆C的方程;
(2)直线l是圆
的任意一条不垂直于坐标轴的切线,l与椭圆C交于A,B两点,若以AB为直径的圆恒过原点,求:
(i)圆O的方程;
(ii)
的最大值.
![](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/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fbbc8f521edab89a7e373287bcfbd9.png)
(1)求椭圆C的方程;
(2)直线l是圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd432589cb00c29cac1806288e99ed0.png)
(i)圆O的方程;
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
您最近一年使用:0次
6 . 椭圆
的右焦点为F、右顶点为A,上顶点为B,且满足
.
(1)求椭圆的离心率
;
(2)设直线
:
与椭圆有唯一公共点
,
与
轴相交于N(N异于M),且
.
(ⅰ)求k的值;
(ⅱ)记O为坐标原点,若
的面积为
,求椭圆的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93e065b3576b3cd585c5fe8410ebfe4.png)
(1)求椭圆的离心率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab760f42892e987055c09495bd014554.png)
(ⅰ)求k的值;
(ⅱ)记O为坐标原点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
您最近一年使用:0次
名校
解题方法
7 . 设椭圆
的离心率为
,且经过点
.
(1)求椭圆
的标准方程;
(2)设直线
与椭圆
交于
两点,
是坐标原点,
,点
刚好在椭圆
上,已知点
的面积为
,求直线
的方程.
![](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/182c81fb1c5e6d1a57a5f34a31ee69a9.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/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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b08819abe43e5c3f833b885a2247d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd6191d6b80be63f3e4d91f9ac78e27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,已知椭圆G:
的、右两个焦点分别为
、
,设
,
,
,若
为正三角形且周长为6.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/d5f05e54-4c28-4b8b-a73e-7e7a2e8d7374.png?resizew=245)
(1)求椭圆G的标准方程;
(2)若过点
且斜率为
的直线与椭圆G相交于不同的两点M、N两点,是否存在实数k使
成立,若存在,求出k的值;若不存在,请说明理由;
(3)若过点
的直线与椭圆G相交于不同的两点M、N两点,记△PMQ、△PNQ的面积记为
、
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/578faa3e92d60d4741a360898e46ce61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bd1719b893f8f64ba2d07e65980b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/025b3e8eb822ee102ac3f61acf646792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/d5f05e54-4c28-4b8b-a73e-7e7a2e8d7374.png?resizew=245)
(1)求椭圆G的标准方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47fb0787422cd572ae13bd0881b6f57a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f544630ecf137a829e34d67be06dbc.png)
(3)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.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/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
2022-10-27更新
|
963次组卷
|
4卷引用:天津市五校联考2023-2024学年高二上学期期中考试数学试题
9 . 椭圆
的右焦点为F、右顶点为A,上顶点为B,且满足
.
(1)求椭圆的离心率
;
(2)直线l与椭圆有唯一公共点M,与y轴相交于N(N异于M).记O为坐标原点,若
,且
的面积为
,求椭圆的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93e065b3576b3cd585c5fe8410ebfe4.png)
(1)求椭圆的离心率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)直线l与椭圆有唯一公共点M,与y轴相交于N(N异于M).记O为坐标原点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab760f42892e987055c09495bd014554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
您最近一年使用:0次
2022-07-25更新
|
15213次组卷
|
17卷引用:天津市河东区天铁第二中学2022-2023学年高二上学期期中模拟数学试题(四)
天津市河东区天铁第二中学2022-2023学年高二上学期期中模拟数学试题(四)2022年新高考天津数学高考真题(已下线)重组卷01天津市第四十七中学2023-2024学年高二下学期第一次阶段性检测(3月)数学试题专题09平面解析几何(第一部分)(已下线)2022年高考天津数学高考真题变式题10-12题(已下线)2022年高考天津数学高考真题变式题19-20题(已下线)第01讲 椭圆(练)(已下线)第04讲 圆锥曲线综合(练)浙江省金华十校2022-2023学年高二上学期期末联考模拟数学试题1(已下线)专题九 平面解析几何-2(已下线)第24讲 圆锥曲线弦长面积问题-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)江西省丰城中学2022-2023学年高二上学期期末数学试题(已下线)考点15 直线与圆锥曲线相切问题 2024届高考数学考点总动员(已下线)第08讲 直线与圆锥曲线的位置关系(练习)陕西省咸阳市武功县普集高级中学2023-2024学年高二上学期12月月考数学试题专题08平面解析几何
名校
解题方法
10 . 已知椭圆C:
(
)的左、右焦点分别为
,
,过
的直线l与椭圆C相交于A,B两点,直线l的倾斜角为45°,
到直线l的距离为
.
(1)求椭圆C的焦距;
(2)若
,求椭圆C的方程.
![](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/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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(1)求椭圆C的焦距;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a8ce713e8c40e21841ee757bb03e4b.png)
您最近一年使用:0次
2022-07-08更新
|
1132次组卷
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12卷引用:天津市河东区2022-2023学年高二上学期期中数学试题
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