1 . 椭圆
:
的离心率为
,圆
:
的周长为
.
(1)求
的方程;
(2)如图,
是
的左焦点,过
的直线交圆O于点M,N,线段
的垂直平分线交C于点P,Q,交
于点A.
(i)证明:四边形
的面积为定值.
(ii)记
,
的面积分别为
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4be819fc47b2aa19ab2022b3dfeb6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557a94abe27623e48ee2c729a8352b8c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(i)证明:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96198405db093eb43952282a69332f92.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46377cebc8defe6d156cc7451f5f1278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f275ea55885ec89eb99fdefec5666c8.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)
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2024-06-05更新
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2卷引用:辽宁省辽阳市辽阳县辽阳石油化纤公司高级中学2024届高三下学期模拟考试数学试题
2 . 已知椭圆
:
的左右顶点分别为
,
,过
的直线与
交于点
,点
在
上,
.
(1)设直线
,
的斜率分别为
,
,求证:
为定值;
(2)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.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/5963abe8f421bd99a2aaa94831a951e9.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e8b17a7840ae7b75590da92fa0965b.png)
(1)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec01614eda195be40a7d5fd494f7f344.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
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名校
3 . 平面几何中有一定理如下:三角形任意一个顶点到其垂心(三角形三条高所在直线的交点)的距离等于外心(外接圆圆心)到该顶点对边距离的2倍.已知
的垂心为D,外心为E,D和E关于原点O对称,
.
(1)若
,点B在第二象限,直线
轴,求点B的坐标;
(2)若A,D,E三点共线,椭圆T:
与
内切,证明:D,E为椭圆T的两个焦点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24e12c97516329a6776fe48c450d93b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c8ef6f3640bd70e40f3b591c8bcc14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b45db8dd8768994af51206565379fd.png)
(2)若A,D,E三点共线,椭圆T:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-05-08更新
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5卷引用:辽宁省抚顺市六校协作体2024届高三下学期5月模拟考试数学试卷
4 . 已知椭圆
,A,B为G的短轴端点,P为G上异于A,B的一点,则直线
,
的斜率之积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda236a74f97b9258ae9cd9f0dd62865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-04-12更新
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3卷引用:辽宁省葫芦岛市2024届高三下学期第一次模拟数学试题
5 . 已知椭圆
的左右焦点分别为
,点
为椭圆
上异于顶点的一动点,
的角平分线分别交
轴、
轴于点
.
(1)若
,求
;
(2)求证:
为定值;
(3)当
面积取到最大值时,求点
的横坐标
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e099a6abe3e9566b2ad385906e323fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ef569668e797b1e94257fd5f4384dd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066b9c12f71ed215ed8e98df05584f76.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b0bac6df5da367c886f57d562c72c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
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2024-02-12更新
|
1976次组卷
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4卷引用:辽宁省丹东市东港市第二中学2024届高三下学期高考热身考试数学试卷
解题方法
6 . 已知如图,点
为椭圆
的短轴的两个端点,且
的坐标为
,椭圆
的离心率为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/acef4fa0-271a-4bd0-814d-7deb9069cc85.png?resizew=176)
(1)求椭圆
的标准方程;
(2)若直线
不经过椭圆
的中心,且分别交椭圆
与直线
于不同的三点
(点
在线段
上),直线
分别交直线
于点
.求证:四边形
为平行四边形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4fd84394e897ebf6c4814b841d427b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/acef4fa0-271a-4bd0-814d-7deb9069cc85.png?resizew=176)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6684304a7537da9517c889c9cbf90a48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d0ff4224f475ab37c6f96d00506f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d107710e7aff959395ca6f8d23c52c7.png)
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2024-01-10更新
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3卷引用:辽宁省沈阳市2023-2024学年高三上学期教学质量监测(一)数学试题
名校
解题方法
7 . 已知椭圆C:
的左顶点为A,上顶点为B,右焦点为
,O为坐标原点,线段OA的中点为D,且
.
(1)求C的方程;
(2)已知点M、N均在直线
上,以MN为直径的圆经过O点,圆心为点T,直线AM、AN分别交椭圆C于另一点P、Q,证明直线PQ与直线OT垂直.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5fa2bb949753445dff343e48283dbab.png)
(1)求C的方程;
(2)已知点M、N均在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
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2023-09-09更新
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11卷引用:辽宁省大连市第二十四中学等校2022届高三高考联合模拟考试数学试题
辽宁省大连市第二十四中学等校2022届高三高考联合模拟考试数学试题重庆市高考康德卷2021届高三模拟调研卷数学试题(三)广东省惠州市2024届高三上学期第一次调研数学试题广东省广州市第六十五中学2024届高三上学期8月摸底数学试题江西省吉安市青原区双校联盟2022-2023学年高二下学期期末考试数学试题福建省南安市蓝园高级中学2022-2023学年高二下学期期末考试数学试题江西省丰城拖船中学2024届高三上学期开学测试数学试题(已下线)专题突破卷23 圆锥曲线大题归类(已下线)重难点突破15 圆锥曲线中的圆问题(四大题型)广东省广州市空港实验中学2024届高三上学期期中数学试题【人教A版(2019)】专题04平面解析几何-高二下学期名校期末好题汇编
8 . 已知定圆F:
,动圆H过点
且与圆F相切,记圆心H的轨迹为C.
(1)求曲线C的方程.
(2)已知
,
,点M是曲线C上异于A、B的任意一点,设直线AM与直线l:
交于点N,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8607b7bdbcb604e6fcfbccb66ed2f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97fb96d52f1ab7cd9c4e9427838bd6e6.png)
(1)求曲线C的方程.
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652e8c360aa4f6aeda334c4b966eda03.png)
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2023-06-06更新
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2卷引用:辽宁省锦州市渤海大学附属高级中学2023届高三第六次模拟考试数学试题
名校
解题方法
9 . 已知椭圆C:
与y轴交于
,
两点,椭圆上异于A,B两点的动点D到A,B两点的斜率分别为
,
,已知
.
(1)求椭圆C的方程;
(2)过定点
与动点D的直线,与椭圆交于另外一点H,若AH的斜率为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42179166d21d549d0a67fc18eb23ddcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578faa3e92d60d4741a360898e46ce61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f213e991614465959aac77292c9bf09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eac9ba606fb477550aa62db7bfa0ac4.png)
(1)求椭圆C的方程;
(2)过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c95021d09eb2b8267a55d5f0461497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8e0773250f233387a78f1ebe6aeab4.png)
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10 . 在
平面上.设椭圆
,梯形
的四个顶点均在
上,且
.设直线
的方程为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/25/76362ac1-d255-42b4-ae6f-107afd6987f4.png?resizew=329)
(1)若
为
的长轴,梯形
的高为
,且
在
上的射影为
的焦点,求
的值;
(2)设
,
,
与
的延长线相交于点
,当
变化时,
的面积是否为定值?若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e09cf640b04531def01fac33b3ae5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7aecaf733d0559d3a03190fc4c7b87.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/25/76362ac1-d255-42b4-ae6f-107afd6987f4.png?resizew=329)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429671166ab81044097fc277f179ee96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bf554d005d0858f819d383d7e7802f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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2023-05-24更新
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2卷引用:辽宁省大连市第二十四中学2023届高三第六次模拟考试数学试卷