名校
解题方法
1 . 已知椭圆
的左右焦点分别为
,以线段
为直径的圆过C的上下顶点,点
在C上,其中e为C的离心率.
(1)求椭圆C的方程和短轴长;
(2)点
在C上,且在x轴的上方,满足
,直线
与直线
的交点为P,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93c13c9d1a1f85ab7a9b044c669bf53.png)
(1)求椭圆C的方程和短轴长;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291255fbc4b2ac36e445fc090bd539b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
您最近一年使用:0次
2024-06-10更新
|
534次组卷
|
2卷引用:2024届河北省承德市部分示范高中高三三模数学试题
名校
解题方法
2 . 已知椭圆
的左顶点到右焦点的距离是3,且
的离心率是
,过左焦点
的直线
与椭圆交于
两点,过左焦点且与直线
垂直的直线
与椭圆交于
两点.
(1)求椭圆
的标准方程;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104ba286d8740a27a3def924432c959a.png)
您最近一年使用:0次
解题方法
3 . 已知椭圆
经过点
和
.
(1)求
的方程;
(2)若点
(异于点
)是
上不同的两点,且
,证明直线
过定点,并求该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea8a480a2fe03293cb8303da8837d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32476e6bf0fed9c3d3f23ebfd40aa693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2024-01-23更新
|
435次组卷
|
5卷引用:河北省承德市2023-2024学年高二上学期期末数学试题
4 . 已知椭圆C:
的右顶点到左焦点
的距离与左焦点
到直线
的距离相等,过椭圆的焦点且与长轴垂直的弦长为3.
(1)求椭圆
的标准方程;
(2)设直线
过点
,且与坐标轴不垂直,与椭圆
相交于P,H两点,线段PH的垂直平分线与
轴交于点
.
①当
时,求直线
的倾斜角的正弦值;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0944c99f34ee41bea845303ed15a7d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc65bd93cb8a2660f538e97a0a8bfdd.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](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)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41121be358df077724fd7009abfdabad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e97c659425a41b13647670327762ea2.png)
您最近一年使用:0次
名校
5 . 已知
,
,动点P满足:直线PM与直线PN的斜率之积为常数
,设动点P的轨迹为曲线
.抛物线
与
在第一象限的交点为A,过点A作直线l交曲线
于点B.交抛物线
于点E(点B,E不同于点A).
(1)求曲线
的方程.
(2)是否存在不过原点的直线l,使点E为线段AB的中点?若存在,求出p的最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accf35598ee054f1bf8b6584641d6d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b2bb30137f92479d11827ee769f001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e393b3e36390b1354950e2cfccc4967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)是否存在不过原点的直线l,使点E为线段AB的中点?若存在,求出p的最大值;若不存在,请说明理由.
您最近一年使用:0次
2021-05-05更新
|
643次组卷
|
3卷引用:河北省承德市2021届高三下学期二模数学试题
6 . 已知椭圆
的两个焦点分别为
,
,离心率为
,过
的直线
与椭圆
交于
,
两点,且
的周长为8.
(1)求椭圆
的方程;
(2)若一条直线与椭圆
分别交于
,
两点,且
,试问点
到直线
的距离是否为定值,证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5585a42c8f07ad90b94ace9db3d78994.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若一条直线与椭圆
![](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/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2020-11-14更新
|
641次组卷
|
19卷引用:河北省承德市隆化县存瑞中学2019-2020学年高三上学期第二次质检数学(文)试题
河北省承德市隆化县存瑞中学2019-2020学年高三上学期第二次质检数学(文)试题【全国百强校】河北省衡水市武邑中学2018-2019学年高二上学期第三次月考数学(文)试题【全国百强校】河北省武邑中学2018-2019学年高二上学期第三次月考数学(理)试题【全国百强校】广西南宁市第二中学2018-2019学年高二下学期期中考试数学(文)试题内蒙古自治区北京八中乌兰察布分校2018-2019学年高二下学期期中考试数学(文)试题陕西省西安市西安中学2019-2020学年高三上学期10月月考数学(文)试题吉林省长春市德惠市九校2019-2020学年高二上学期期中数学(理)试题重庆市朝阳中学2019-2020学年高二上学期12月月考数学试题2020届黑龙江省双鸭山市第一中学高三上学期期末数学(文)试题2020届广东省佛山市第一中学高三上学期期中数学(文)试题河北省张家口市第一中学2018-2019学年高一衔接班下学期期末数学试题内蒙古包头市包钢四中2018-2019学年高二下学期4月月考数学(文)试题吉林省吉化第一高级中学校2019-2020学年高二上学期期中数学(理)试题安徽省亳州市涡阳县育萃中学2020-2021学年高二上学期第二次月考数学试题陕西省咸阳市实验中学2020-2021学年高二上学期第四次月考数学(理)试题湖北省石首市2019-2020学年高二下学期期中数学试题陕西省咸阳市武功县普集高中2021-2022学年高二上学期第三次月考理科数学试题(已下线)第03讲 复习课-圆锥曲线与方程-【寒假自学课】2022年高二数学寒假精品课(苏教版2019选择性必修第二册)四川省内江市威远中学2022-2023学年高二下学期第二次阶段性考试数学(文)试题
2013·辽宁沈阳·一模
名校
7 . 已知直线
经过椭圆
:
的左顶点
和上顶点
,椭圆
的右顶点为
,点
是椭圆
上位于
轴上方的动点,直线
与直线
分别交于
两点.
(1)求椭圆方程;
(2)求线段
的长度的最小值;
(3)当线段
的长度最小时,在椭圆上有两点
,使得
,
的面积都为
,求直线
在y轴上的截距.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18feaed4f3dd7698210ba302c81dca6d.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](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/11b141148d19998c842aee2e5b1de63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7e7a5ecd65d4eb785e543dd7eeea85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(1)求椭圆方程;
(2)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(3)当线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5dd698ddbe275267809650dc551e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407c7ae7ac3d1445b1edc0579c97f3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9da30de49f519f37c78bb0ae35c0e53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9d5f7ba174f6ec3e7d9a105868126c.png)
您最近一年使用:0次
2019-10-02更新
|
621次组卷
|
6卷引用:河北省承德第一中学2019-2020学年高二9月月考数学试题
名校
8 . 已知椭圆
的短轴长为2,且椭圆
过点
.
(1)求椭圆
的方程;
(2)设直线
过定点
,且斜率为
,若椭圆
上存在
两点关于直线
对称,
为坐标原点,求
的取值范围及
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f04443a0c1cf4808aea741c9f9379b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d623f0a96a198bcba5cb629a6c58e34.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/bab2951a953fa8c2b971de027870e83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b93eb31a8bb0dcf55440f2ccfda45e.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2981bf2261343f905ec1b5355a3c4.png)
您最近一年使用:0次
2018-02-04更新
|
342次组卷
|
2卷引用:河北省承德市联校2017-2018学年高二上学期期末考试数学(理)试题
9 . 已知椭圆
的一个焦点为
.设椭圆
的焦点恰为椭圆
短轴的顶点,且椭圆
过点
.
(1)求
的方程及离心率;
(2)若直线
与椭圆
交于
两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba756b26c3145611b8b7b0e165e9bad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63309dbc3612815f6dbdee23d9a10adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d4c612cdb0a8d2634c81dab98cc38.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026808536f6b6d265c778e23836fbf13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b2fbd3ec98d50685c882b7d7095523.png)
您最近一年使用:0次
名校
10 . 已知离心率为
的椭圆
的一个焦点坐标为
.
(1)求椭圆
的标准方程;
(2)过点
的直线
与轨迹
交于不同的两点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b36a0866ec5fbb94e6cf4d61579e0b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.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/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aaa6f76638d1c72d222501e18f42807.png)
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2017-11-15更新
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4卷引用:河北省承德第一中学2020-2021学年高二上学期第二次月考数学试题