1 . 已知椭圆C:
的右顶点为
,过左焦点F的直线
交椭圆于M,N两点,交
轴于P点,
,
,记
,
,
(
为C的右焦点)的面积分别为
.
(1)证明:
为定值;
(2)若
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a98eaaab44a91d0bad21dbd260be770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2dc32a930595d3e6d87ac24701a9364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348907f672c64a4563ce9e9e5edd53b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a79adfd9e2b87b864803e4505d2a0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9946d1ce220afa1625ebb09c34b56c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed0ccdab6cfb38a35f9dea720df03c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a07a2f0db1140e0588aa19f7884ba5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48559d27a71801cef4c97312886d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-11-23更新
|
1723次组卷
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8卷引用:重庆市2023届高三下学期第一次联考数学试题
重庆市2023届高三下学期第一次联考数学试题湖南省郴州市原创试题评比参评2022届高三高考模拟数学试题(安仁一中命制)福建省三校联考2022-2023学年高二上学期期中考试数学试题(已下线)数学(新高考Ⅰ卷B卷)江苏省南京市雨花台中学2022-2023学年高三上学期期中数学试题(已下线)专题13 圆锥曲线压轴解答题常考套路归类(精讲精练)-3(已下线)模块六 专题8 易错题目重组卷(重庆卷)辽宁省沈阳市浑南区东北育才学校试验部2023-2024学年高二上学期12月月考数学试题
名校
解题方法
2 . 如图所示,在
中,
在线段BC上,满足
,
是线段
的中点.
交
于点Q(图1),求
的值;
(2)过点
的直线与边
,
分别交于点E,F(图2),设
,
.
(i)求证
为定值;
(ii)设
的面积为
,
的面积为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e90f4770bcae68f4d17a3e94d4b521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3791f7eb4d33d52bf7a73c1b3e75f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efec6ba8a1f02735c949442bdf3a1989.png)
(2)过点
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172a147172824e510e81e27500f998d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5cf7b94ee40cfb499d1f06d6a14fb4.png)
(i)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a58464a16629aa18aa99187cb0d398.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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
2022-04-23更新
|
2273次组卷
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12卷引用:重庆市巴南区部分学校2023-2024学年高一下学期阶段测试数学试题
重庆市巴南区部分学校2023-2024学年高一下学期阶段测试数学试题浙江省A9协作体2021-2022学年高一下学期期中联考数学试题黑龙江省佳木斯市第一中学2022-2023学年高二上学期开学调研考试数学试题上海市金山中学2021-2022学年高一下学期期末数学试题(已下线)6.3.1平面向量基本定理(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)福建省福州第一中学2022-2023学年高一下学期期中考试数学模拟试题(已下线)模块二 专题1 《平面向量》单元检测篇 B提升卷 (苏教版)江苏省无锡市四校2022-2023学年高一下学期期中联考数学试题河南省周口市太康县第一高级中学2022-2023学年高一下学期2月月考数学试题(已下线)专题05 平面向量基本定理-《重难点题型·高分突破》(苏教版2019必修第二册)(已下线)第一次月考解答题压轴题十六大题型专练(1)-举一反三系列(人教A版2019必修第二册)(已下线)8.1 向量的概念和线性运算-同步精品课堂(沪教版2020必修第二册)
名校
3 . 在△ABC中,点D,E,F分别在边AB,BC,AC上,且
,
,
,P是CD,EF的交点.设
,
.
(1)用
,
表示
,
;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cadd71e033cdf5d80936ca1cb4398dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdf0a9eef16e289e64e65adaa8e0b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a113dc62db61e60349255fe830db6cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae92f0c583cc9daf980a8621ad96aef5.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ed9c2e9fabbfc63733bae8fa079d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b5a51e65e9b56a9970de33ead263a9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3134c63f85a55d94233e95198c3e6491.png)
您最近一年使用:0次
2022-04-22更新
|
594次组卷
|
3卷引用:重庆市缙云教育联盟2023-2024学年高二上学期9月月度质量检测数学试题
重庆市缙云教育联盟2023-2024学年高二上学期9月月度质量检测数学试题河南省创新发展联盟2021-2022学年高一下学期联考(三)数学试题(已下线)专题05 平面向量基本定理-《重难点题型·高分突破》(苏教版2019必修第二册)
名校
解题方法
4 . 在
中,
为
所在平面内的两点,
,
.
(1)以
和
作为一组基底表示
,并求
;
(2)
为直线
上一点,设
,若直线
经过
的垂心,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ee5e734d09865db65a44576927b8fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d68623c37320af188b166ebcef353e.png)
(1)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c973e310e577bd11972a15e81c206b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482cf4a5151ecce1b8a91b463d2b2cc2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8601f33113b059d6e05eee963a2d4c62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
您最近一年使用:0次
2021-06-20更新
|
1728次组卷
|
8卷引用:重庆市缙云教育联盟2021-2022学年高一下学期4月质量检测数学试题
重庆市缙云教育联盟2021-2022学年高一下学期4月质量检测数学试题山东省青岛市青岛第一中学2020-2021学年高一下学期期中数学试题山东省青岛胶州市2020-2021学年高一下学期期中考试数学试题安徽省六安市第一中学2021-2022学年高二上学期开学考试数学试题江西省宁冈中学2020-2021学年高二上学期期中考试数学(理)试题(已下线)高一数学下学期期中精选50题(压轴版)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)江苏省镇江中学2022-2023学年高一下学期4月期中数学试题(已下线)高一下期中真题精选(压轴60题专练)-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)
名校
解题方法
5 . 已知椭圆
:
(
),
为坐标原点,长轴长为4,离心率
.
(1)求椭圆
的方程;
(2)设直线
的方程为:
,点
为椭圆
在
轴正半轴上的顶点,过点
作
,垂足为
,点
在椭圆上(不同于点
)且满足:
,求直线
的斜率
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.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/f1d0aafd52e26c241c46d0206f42f415.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae781496bb5bc79b67abced9aa3cd0c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e6f618ec5f7586755022b10a7e8322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
6 . 在
中,
为直角,
,
,
与
相交于点
,
,
.
(1)试用
、
表示向量
;
(2)在线段
上取一点
,在线段
上取一点
,使得直线
过
,设
,
,求
的值;
(3)若
,过
作线段
,使得
为
的中点,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2981bf2261343f905ec1b5355a3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c607be8fbe8b2701e0451e9322223e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca7757b00ff2bdc8796ccfa33fec0293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6942bd9fc5d090de0cfad7022aa32f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cc63e33fe47da2704cff57d148dde0.png)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00da1c29aea46e36cda0f5780966bb6.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f9c6f622be010cd1d9cc5c13f4fd9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23438690dec68d60e07d2ab6bdbf1d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ebeb198e80f9c2e6406f0601554b92.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228f00eb81c06f6862e15e923109c35b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2d713292dd1f9f367d382077c703d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3b182fcad057f49f2360d6d2b4dddf.png)
您最近一年使用:0次
2019-12-10更新
|
1054次组卷
|
6卷引用:重庆市铜梁区第一中学2020-2021学年高一下学期3月月考数学试题
名校
7 . 在平面直角坐标系
中,
分别为椭圆
:
的左、右焦点,
为短轴的一个端点,
是椭圆
上的一点,满足
,且
的周长为
.
(1)求椭圆
的方程;
(2)设点
是线段
上的一点,过点
且与
轴不垂直的直线
交椭圆
于
两点,若
是以
为顶点的等腰三角形,求点
到直线
距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68f672662d8c3fd87feea75866dcebc.png)
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/2017/7/19/1733456931889152/1735517746724864/STEM/d04a87fddba04970af7f7898c9408e6b.png?resizew=120)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664be7ccdc9d0c5305a7d308749e53a4.png)
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(1)求椭圆
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(2)设点
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您最近一年使用:0次
2017-07-22更新
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622次组卷
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2卷引用:重庆市育才中学2019-2020学年高三上学期第一次月考数学试题