1 . 已知椭圆
的离心率
,且椭圆过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8da36e3081bfe5d32c9ec70be4da3da.png)
(1)求椭圆
的标准方程;
(2)设直线
与
交于
、
两点,点
在椭圆
上,
是坐标原点,若
,判定四边形
的面积是否为定值?若为定值,求出该定值;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8da36e3081bfe5d32c9ec70be4da3da.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c8bd916b5945fee04c1acb26f8ac86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7346144de4c74f6b8bb14bea9ebd41.png)
您最近一年使用:0次
2020-02-18更新
|
4222次组卷
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21卷引用:宁夏中卫市中宁县2022-2023学年高二上学期质量测查(期末)数学(理)试题
宁夏中卫市中宁县2022-2023学年高二上学期质量测查(期末)数学(理)试题【市级联考】湖南省郴州市2019届高三第三次质量检测数学(文)试题【市级联考】陕西省榆林市2019届高三第四次普通高等学校招生模拟考试文科数学试题2020届河南省南阳市高三上学期期末数学(理)试题2020届河南省信阳市高三第二次教学质量检测数学(理)试题2019届湖南省长沙市雅礼中学高三下学期5月月考数学(文)试题2019届陕西省榆林市高三第四次模拟考试数学(文)试题(已下线)提升套餐练05-【新题型】2020年新高考数学多选题与热点解答题组合练(已下线)冲刺卷05-决战2020年高考数学冲刺卷(山东专版)2019届吉林省普通高三第三次联合模拟数学(文)试题2020届河南省开封市第五中学高三第四次教学质量检测数学(理)试卷(已下线)专题31 圆锥曲线中的定点、定值、探索性问题-冲刺2020高考跳出题海之高三数学模拟试题精中选萃(已下线)专题06 解析几何中的定点、定值问题(第五篇)-备战2020年高考数学大题精做之解答题题型全覆盖2020届黑龙江省大庆实验中学高三第一次模拟数学(文)试题河南省信阳市2020届高三上学期第二次教学质量检测(期末)数学(文)试题湖南省邵阳市邵东县第一中学2020-2021学年高三上学期第二次月考数学试题湖南省长沙市明德中学2019-2020学年高二上学期期中数学试题苏教版(2019) 选修第一册 选填专练 第3章 微专题七 高考中圆锥曲线问题(3):证明与探索性问题河南省许平汝联盟2021-2022学年高三下学期4月模拟考试文科数学试题河南省鹤壁市浚县第一中学2021-2022学年高三下学期4月考试文科数学试题江西省信丰中学2021-2022学年高二下学期第一次月考数学(理)B层试题
名校
2 . 已知椭圆方程为
.
(1)设椭圆的左右焦点分别为
、
,点
在椭圆上运动,求
的值;
(2)设直线
和圆
相切,和椭圆交于
、
两点,
为原点,线段
、
分别和圆
交于
、
两点,设
、
的面积分别为
、
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c03c6b8d7418edf20f474389971352.png)
(1)设椭圆的左右焦点分别为
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eba1465d885dfaa659828849c76e216.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.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/9fd2981bf2261343f905ec1b5355a3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4459eaa92f139d29880307b21e9b7611.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
2020-01-30更新
|
1195次组卷
|
5卷引用:宁夏回族自治区银川一中2020届高三第四次模拟考试数学(理)试题
名校
3 . 已知圆
,圆
,动圆P与圆M外切并且与圆N内切,圆心P的轨迹为曲线C.
(1)求曲线C的方程;
(2)设不经过点
的直线l与曲线C相交于A,B两点,直线QA与直线QB的斜率均存在且斜率之和为-2,证明:直线l过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0436f3462eba465ba4e6f7b787776b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c952b4a8f7fbfd9beb36b83e80d0adb.png)
(1)求曲线C的方程;
(2)设不经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfdd693d7bc86f35cd51275c0962ed5.png)
您最近一年使用:0次
2020-01-29更新
|
2937次组卷
|
10卷引用:2020届宁夏六盘山高级中学高三下学期第二次模拟考试数学(文)试题
2020届宁夏六盘山高级中学高三下学期第二次模拟考试数学(文)试题2020届安徽省池州市高三上学期期末考试数学(理)试题2020届安徽省池州市高三上学期期末考试数学(文)试题2020届高三2月第01期(考点08)(理科)-《新题速递·数学》安徽省安庆一中2019-2020学年高三下学期阶段性检测理科数学试题广东省深圳市高级中学2019-2020学年高三下学期3月线上模拟数学(文)试题四川省绵阳中学2021-2022学年高三上学期第二次模拟检测理科数学试题(已下线)专题30 圆锥曲线求过定点大题100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)江苏省南通市如皋市2024届高三上学期期初考试押题卷数学试题(已下线)热点7-2 椭圆及其应用(8题型+满分技巧+限时检测)
名校
4 . 已知椭圆
:
的右焦点为
,且经过点
.
(1)求椭圆
的方程以及离心率;
(2)若直线
与椭圆
相切于点
,与直线
相交于点
.在
轴是否存在定点
,使
?若存在,求出点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
(1)求椭圆
![](https://img.xkw.com/dksih/QBM/2020/1/11/2374595627982848/2374832739950592/STEM/762222e747bb4784af7100a3aeb0431e.png?resizew=16)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236bfabaa6ba7ad70803a85b6d422608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-01-11更新
|
726次组卷
|
6卷引用:宁夏银川二十四中2021届高三二模数学(文)试题
名校
5 . 如图,在平面直角坐标系xOy中,已知椭圆
的离心率为
,右焦点到直线
的距离为1.
![](https://img.xkw.com/dksih/QBM/2019/12/31/2367237573689344/2367715206365184/STEM/c683e78aed2c4bacb6bc21220374daab.png?resizew=213)
求椭圆的标准方程;
若P为椭圆上的一点
点P不在y轴上
,过点O作OP的垂线交直线
于点Q,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78c38805c09dcfbcc42103308975a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b19458962722f1e812d5c5006740d0c.png)
![](https://img.xkw.com/dksih/QBM/2019/12/31/2367237573689344/2367715206365184/STEM/c683e78aed2c4bacb6bc21220374daab.png?resizew=213)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6bebad2e831ff4930b1f221d1abf57d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae50d614a8afd23b30069c46f78787a3.png)
您最近一年使用:0次
2020-01-01更新
|
267次组卷
|
2卷引用:宁夏中卫市2021届高三第二次优秀生联考数学(文)试题
名校
6 . 在平面直角坐标系
中,已知椭圆
的离心率为
,点
在椭圆
上.
(1)求椭圆
的方程;
(2)设直线与圆
相切,与椭圆
相交于
两点,求证:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10aa98b163ade82dcadbe8dd3b73e42e.png)
您最近一年使用:0次
2019-12-08更新
|
2122次组卷
|
8卷引用:2020届宁夏石嘴山市第三中学高三上学期期末数学(理)试题
7 . 在直角坐标系xOy中,动点P与定点
的距离和它到定直线
的距离之比是
,设动点P的轨迹为E.
(1)求动点P的轨迹E的方程;
(2)设过F的直线交轨迹E的弦为AB,过原点的直线交轨迹E的弦为CD,若
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求动点P的轨迹E的方程;
(2)设过F的直线交轨迹E的弦为AB,过原点的直线交轨迹E的弦为CD,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1791846aaa3ff3c22c9d751a6500275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b014b0be63514079243a914c7d20e.png)
您最近一年使用:0次
2019-11-14更新
|
1141次组卷
|
5卷引用:宁夏回族自治区银川市兴庆区银川一中2019-2020学年高三第五次月考数学(文)试题
名校
8 . 已知椭圆
,若不与坐标轴垂直的直线
与椭圆
交于
两点.
(1)若线段
的中点坐标为
,求直线
的方程;
(2)若直线
过点
,点
满足
(
分别是直线
的斜率),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb7101fa9146fdec51d44b8bf481dc7.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)
(1)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb13bbc5335efc427f9c619a51dae3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c9b882323edba16b3625458239b6f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60aa565837563f82bf1f791288a36250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbc850dc78495bc675e298211c4a0fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2019-10-03更新
|
810次组卷
|
4卷引用:宁夏回族自治区银川市兴庆区宁一中2019-2020学年高二上学期期中数学(理)试题
名校
9 . 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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
(1)求椭圆
的方程;
(2)若直线
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/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ea349843c7e14e655a0d950bbf9094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.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/15b256345d7109e081b7c895591e995d.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/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
2019-06-24更新
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1123次组卷
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5卷引用:宁夏吴忠市吴忠中学2021-2022学年高二下学期期中考试数学(文)试题
名校
10 . 已知斜率为1的直线
与椭圆
交于
,
两点,且线段
的中点为
,椭圆
的上顶点为
.
(1)求椭圆
的离心率;
(2)设直线
与椭圆
交于
两点,若直线
与
的斜率之和为2,证明:
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3860d9fa9fe43eeecea30202d880f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cf7358675528bc6342a378563a197a8.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/23a44baceab9e1d74f6ca53aea8c4d72.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/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
您最近一年使用:0次
2019-06-15更新
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1130次组卷
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6卷引用:宁夏银川三沙源上游学校2019-2020学年高二上学期第二次月考数学(理)试题