1 . 已知椭圆
离心率为
,椭圆M与y轴交于A,B两点(A在下方),且
过点
直线l与椭圆M交于C,D两点(不与A重合).
(Ⅰ)求椭圆M的方程;
(Ⅱ)证明:直线
的斜率与直线
的斜率乘积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cf6cca367ce2afd96d7d951f9587e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78dc1c1ee60be772884f9d69804f56da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dbbb76c7a42b124d474b652abdbadde.png)
(Ⅰ)求椭圆M的方程;
(Ⅱ)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2020-09-04更新
|
1812次组卷
|
6卷引用:湖北省黄石市第一中学2019-2020学年高二下学期期末数学试题
湖北省黄石市第一中学2019-2020学年高二下学期期末数学试题北京市昌平区2020届高三第二次统一练习(二模)数学试题(已下线)【新教材精创】2.8+直线与圆锥曲线的位置关系(2)-A基础练-人教B版高中数学选择性必修第一册(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)广东省雷州市第二中学2020-2021学年高二上学期期中数学试题北京市中关村中学2022届高三下学期开学测试数学试题
名校
解题方法
2 . 已知点
,
是椭圆
的左,右焦点,椭圆上一点
满足
轴,
,
.
(1)求椭圆
的标准方程;
(2)过
的直线
交椭圆
于
两点,当
的内切圆面积最大时,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/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa9a6be97b5f275d55697fd3cd0a442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956c0b3335922c0586a101dfdb8fdea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b1a324748fa3786fa709db3b008e6d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/d3c07ebcbfacda073208d483c58e8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-05-09更新
|
739次组卷
|
9卷引用:湖北省黄冈中学2020届高三下学期6月第三次模拟考试文科数学试题
湖北省黄冈中学2020届高三下学期6月第三次模拟考试文科数学试题2020届安徽省皖南八校高三第三次联考数学(理)试题2020届安徽省皖南八校高三第三次联考数学(文)试题贵州省凯里实验高级中学2020-2021学年高二下学期第一次月考数学(文)试题贵州省凯里实验高级中学2020-2021学年高二下学期第一次月考数学(理)试题四川省成都市锦江区嘉祥外国语高级中学2022-2023学年高三上学期期中数学理科试题四川省成都市锦江区锦江区嘉祥外国语高级中学2022-2023学年高三上学期期中数学试题宁夏银川市永宁县第二中学高级中学2021届高考数字诊断性文科试题江西省上高二中2023届高三上学期第四次月考数学(理)试题
解题方法
3 . 已知椭圆
的离心率为
,右焦点为
,三角形
的三个顶点都在椭圆上,设它的三条边
、
、
的中点分别为
、
、
,且三条边所在直线的斜率分别为
.若直线
、
、
的斜率之和为-1(
为坐标原点),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dddcb841e17cc8df9c1aa78bc1b12c1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](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/85bc4b826bb67df8095917ffdb764008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dddcb841e17cc8df9c1aa78bc1b12c1.png)
您最近一年使用:0次
名校
解题方法
4 . 已知抛物线
与过点
的直线
交于
两点.
(1)若
,求直线
的方程;
(2)若
,
轴,垂足为
,探究:以
为直径的圆是否过定点?若是,求出该定点的坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a1f104a61443087fe9ae9481d47c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04cfb624767e0fdee6b8c1a755816376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28144f4eee678c7f2688b21261149d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2020-04-19更新
|
532次组卷
|
6卷引用:湖北省武汉市江夏一中、汉阳一中2019-2020学年高三下学期4月联考文科数学试题
名校
5 . 在直角坐标系
中,已知
分别是椭圆
的左、右焦点,
的离心率是
,直线
与C相交于
两点.
(1)当
经过
且
时,求
的值;
(2)记直线
的斜率分别为
,若
,试求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](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/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f9515cfa7042107ed0ea7a3e409b91c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091145fcc157587a3fc8e0b7c7c0ecb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42623f14667ebfa914eb12d026023d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcb71b9faccca05307b72582a3be8cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cd0efc142e3abb0d8f21e6447f0a7a.png)
您最近一年使用:0次
名校
6 . 已知椭圆
过点
.
(Ⅰ)求椭圆
的方程,并求其离心率;
(Ⅱ)过点
作
轴的垂线
,设点
为第四象限内一点且在椭圆
上(点
不在直线
上),直线
关于
的对称直线
与椭圆交于另一点
.设
为坐标原点,判断直线
与直线
的位置关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c228de3980a482944511f1138333970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4754fbe523ca63eba3810a3f88f37df3.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)过点
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
您最近一年使用:0次
2020-01-10更新
|
947次组卷
|
11卷引用:【市级联考】湖北省十堰市2019届高三模拟试题文科数学试题
【市级联考】湖北省十堰市2019届高三模拟试题文科数学试题【区级联考】北京市东城区2019届高三第一学期期末数学(理)试题四川省成都市棠湖中学2018-2019学年高二下学期期末考试数学(文)试题四川省成都市成都外国语学校2019-2020学年高三期中数学(理)试题四川省成都市成都外国语学校2019-2020学年高三上学期期中数学(文)试题(已下线)2020届高三12月第01期(考点08)(理科)-《新题速递·数学》天津市河北区2018-2019学年度高三年级总复习质量检测(二)数学(理)试题2020届黑龙江省实验中学高三下学期开学考试数学(文)试题(已下线)专题18 圆锥曲线(解答题)-2020年高考数学母题题源解密(天津专版)四川省内江市2021届高三第三次模拟数学(文)试题北京市石景山区2019-2020学年高三上学期期末考试数学试题
名校
7 . 已知
的两个顶点为
,
,平面内P,Q同时满足
;
;
.
求顶点A的轨迹E的方程;
过点
作两条互相垂直的直线
,
,直线
,
被点A的轨迹E截得的弦分别为
,
,设弦
,
的中点分别为M,
试问:直线MN是否恒过一个顶点?若过定点,请求出该顶点,若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408ff0716718d8d85ca02bf29e04f2ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e19833fdc4c36aa48cb3d0388be994b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda76cae3833856c83f2b20de6446ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb38523cc792a440e6abb5ff47789373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798f50a2fba2dc70b257d5e788fd85c3.png)
![](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/9963b39f135bfeca3de65460c94546c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8f64ebec4a71a609204458cc54df82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea5c8fe935beac660eda538e59cd43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8f64ebec4a71a609204458cc54df82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea5c8fe935beac660eda538e59cd43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc689a0bf91e6384ca0bd3fb3fbfa0ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41d95f9da0a01f1d66eaad79f551e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc689a0bf91e6384ca0bd3fb3fbfa0ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41d95f9da0a01f1d66eaad79f551e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cca556f98c82b70c177d41cc31b217c.png)
您最近一年使用:0次
8 . 已知椭圆
(a>b>0)的左右焦点分别为F1,F2,图象经过点A(2,0)和点B(0,
)过F2与坐标轴不垂直的直线l与椭圆C交于P,Q两点,N为PQ的中点.
(1)求椭圆C的方程;
(2)设点
,且MN⊥PQ于N,求直线PQ的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6c9d1b8c7214c121f6724cc0cf01df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3f8c3ba00c59e0634ed10fa85289de.png)
(1)求椭圆C的方程;
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a617b86803011c84f1abb46fe4967d.png)
您最近一年使用:0次
解题方法
9 . 如图,已知椭圆
,斜率为﹣1的直线与椭圆C相交于A,B两点,平行四边形OAMB(O为坐标原点)的对角线OM的斜率为
,则椭圆的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/97fba536-07d4-4374-9252-719331a292d9.png?resizew=207)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4294843dc627c5063a09ab944b5dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb84f6fbac102ccf326b2223d69cb7cc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/97fba536-07d4-4374-9252-719331a292d9.png?resizew=207)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-12-15更新
|
941次组卷
|
2卷引用:湖北省襄阳市2019-2020学年高二上学期期末数学试题
10 . 已知图
,
,斜率为1的直线
分别交椭圆
,
于
(如图),
为坐标原点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/ca72f601-e52c-4386-99ef-79f55964c1ad.png?resizew=190)
(1)证明:
;
(2)若
与
的面积相等,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0ad41722598d9fd00138a0f781b5df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc5f7e05d956c36a2b75c9bc5e7a19f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/ca72f601-e52c-4386-99ef-79f55964c1ad.png?resizew=190)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd82bf82c3254c27b00f65b9a697e0d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7ffcd1925a2b1259221c6a476152f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2019-11-30更新
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281次组卷
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2卷引用:湖北省部分重点中学2019-2020学年高三上学期第一次联考考数学(文)试题