1 . 已知曲线
,直线
与曲线
交于
轴右侧不同的两点
.
(1)求
的取值范围;
(2)已知点
的坐标为
,试问:
的内心是否恒在一条定直线上?若是,请求出该直线方程;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff63bffc106e06fd2629a3d35c637f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
您最近一年使用:0次
2023-04-01更新
|
2286次组卷
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6卷引用:福建省泉州市安溪铭选中学2024届高三下学期4月质量检测数学试题
福建省泉州市安溪铭选中学2024届高三下学期4月质量检测数学试题山东省新高考联合质量测评2023届高三下学期3月联考数学试题江苏省四校(无锡市辅仁高级中学、江阴高中、宜兴一中、常州市北郊中学)2022-2023学年高三下学期4月阶段性测试数学试题(已下线)专题15圆锥曲线中的定点、定值、证明问题(已下线)模块六 专题5易错题目重组卷(江苏卷)(已下线)重难点突破16 圆锥曲线中的定点、定值问题 (十大题型)-2
名校
解题方法
2 . 已知椭圆
的右顶点为A,左焦点为F,过点F作斜率不为零的直线l交椭圆于
两点,连接
,
分别交直线
于
两点,过点F且垂直于
的直线交直线
于点R.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/66d2811b-202b-4abb-b9e7-939080908ed3.png?resizew=216)
(1)求证:点R为线段
的中点;
(2)记
,
,
的面积分别为
,
,
,试探究:是否存在实数
使得
?若存在,请求出实数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb4717d7fa6d522090c5e949f650bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051be09b4e835cf68f624541a843018d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051be09b4e835cf68f624541a843018d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/66d2811b-202b-4abb-b9e7-939080908ed3.png?resizew=216)
(1)求证:点R为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d7bc44c23548b83970d3422817be1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a62d1f44c3ec83f280aa3b76d17b152b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dbdbc43aa8c6cc90d93a6d8010ef07f.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/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9704598bcc28d88271fee9b2b354254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-03-09更新
|
2264次组卷
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5卷引用:福建省厦门双十中学2023届高三高考适应性考试数学试题
3 . 已知椭圆
的左、右顶点分别为A,B.直线l与C相切,且与圆
交于M,N两点,M在N的左侧.
(1)若
,求l的斜率;
(2)记直线
的斜率分别为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812af758672db7576ad2a72eb1061248.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e4d7503a7d57ba242ad4e05c7006a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
您最近一年使用:0次
2023-03-09更新
|
1067次组卷
|
3卷引用:福建省泉州市2023届高三数学质量监测试题(三)
4 . 已知椭圆C:
(a>b>0)的离心率为
,左、右焦点分别为F1,F2,过F1的直线l交C丁A.B两点.当l⊥x轴时,△ABF2的面积为3.
(1)求C的方程;
(2)是否存在定圆E,使其与以AB为直径的圆内切?若存在,求出所有满足条件的圆E的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3d2ee2a9563d156141fec8e8439352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求C的方程;
(2)是否存在定圆E,使其与以AB为直径的圆内切?若存在,求出所有满足条件的圆E的方程;若不存在,请说明理由.
您最近一年使用:0次
2023-03-07更新
|
1320次组卷
|
3卷引用:福建省厦门市2023届高三下学期第二次质量检测数学试题
5 . 已知
的上顶点到右顶点的距离为
,离心率为
,右焦点为F,过点F的直线(不与x轴重合)与椭圆C相交于A、B两点,直线
与x轴相交于点H,过点A作
,垂足为D.
(1)求椭圆C的标准方程;
(2)①求四边形OAHB(O为坐标原点)面积的取值范围;
②证明直线BD过定点E,并求出点E的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbd8a5d973b7a54b7605388fdcfbb07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13b505788d3d02bf232ac637fc3a8ee.png)
(1)求椭圆C的标准方程;
(2)①求四边形OAHB(O为坐标原点)面积的取值范围;
②证明直线BD过定点E,并求出点E的坐标.
您最近一年使用:0次
2022-08-29更新
|
1205次组卷
|
10卷引用:福建省厦门外国语学校2023届高三上学期第一次月考数学试题
福建省厦门外国语学校2023届高三上学期第一次月考数学试题福建省三明第一中学2023届高三上学期期中考试数学试题陕西省咸阳市武功县普集高级中学2023届高三下学期五模理科数学试题(已下线)第五篇 向量与几何 专题8 帕斯卡定理、布列安桑定理、笛沙格定理、彭塞列闭合定理 微点4 塞瓦定理、富瑞基尔定理山东省东营市第一中学2021-2022学年高二上学期期中数学试题河南省巩义市重点校2022-2023学年高二上学期第四次考试数学试题河南省郑州市新密市第一高级中学2022-2023学年高二上学期第三次月考数学试题山西省汾阳市育才中学2022-2023学年高二上学期第二次学情检测数学试题(已下线)第24讲 圆锥曲线弦长面积问题-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)云南省临沧市民族中学2022-2023学年上学期高二第三次月考数学试题
名校
解题方法
6 . 如图,在平面直角坐标系中,O为原点,
,过直线l:
左侧且不在x轴上的动点P,作
于点H,
的角平分线交x轴于点M,且
,记动点P的轨迹为曲线C.
![](https://img.xkw.com/dksih/QBM/2022/5/2/2970937454297088/2973345847992320/STEM/860671dd-d46e-417c-a853-fbcf5f41dc84.png?resizew=206)
(1)求曲线C的方程;
(2)已知曲线C与x轴正半轴交于点
,过点
的直线
交C于A,B两点,
,点T满足
,其中
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055a2ef09e2ee0948cf67c58de58732d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a431edd18debb185c471b0efd95ed171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7854ee62049c4e0116055d1ad70fe0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9673c58e8ca3abd1d13a5efa29dfa433.png)
![](https://img.xkw.com/dksih/QBM/2022/5/2/2970937454297088/2973345847992320/STEM/860671dd-d46e-417c-a853-fbcf5f41dc84.png?resizew=206)
(1)求曲线C的方程;
(2)已知曲线C与x轴正半轴交于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe46eb6357808db0b783464dca4c7cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e37c79ee7a735f2de653113a36a44a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b28850fe78e68997fec2c7a44b00a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30f3f4ea810522864ff39ec882d4524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc75ebb433d388d43637b4faa72f4f5e.png)
您最近一年使用:0次
2022-05-06更新
|
1201次组卷
|
4卷引用:福建省三明市普通高中2022届高三5月质量测试数学试题
福建省三明市普通高中2022届高三5月质量测试数学试题(已下线)考点23圆锥曲线综合应用-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)(已下线)专题37 求曲线的轨迹方程-2重庆市第八中学校2022-2023学年高三上学期期中学情检验数学试题
7 . 在平面直角坐标系
中,已知椭圆
的左、右焦点为
,离心率为
.过点
作直线
与椭圆
相交于
两点.若
是椭圆
的短轴端点时,
.
(1)求椭圆
的标准方程;
(2)试判断是否存在直线
,使得
,
,
成等差数列?若存在,求出直线
的方程;若不存在,说明理由.
![](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/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb4f6fdb607995852c4b725dd039b4e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)试判断是否存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4051a41af7b7dc6ddcabb36d3dd01d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a0a23d1ef1f655f1e38423f66cf9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea26749567cb5c2deb76fef293148d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-04-27更新
|
1782次组卷
|
3卷引用:福建省2022届高三毕业班4月百校联合测评数学试题
名校
解题方法
8 . 如图,已知抛物线
的焦点为椭圆
:
(
)的右焦点
,点
为抛物线与椭圆
在第一象限的交点,且
.
的方程;
(2)过点
的直线
交抛物线于
,
两点,交椭圆于
,
两点(
,
,
,
依次排序),且
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2afb1ac69a88a2532707f81197fd17d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](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/5963abe8f421bd99a2aaa94831a951e9.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/8455657dde27aabe6adb7b188e031c11.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6d5cb912b6c37055ed3d13033530e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-02-28更新
|
1309次组卷
|
7卷引用:福建省三明市第一中学2022届高三5月质量检测数学试题
名校
解题方法
9 . 已知斜率为
的直线交椭圆
于A,
两点,
的垂直平分线与椭圆交于
,
两点,点
是线段
的中点.
(1)若
,求直线
的方程以及
的取值范围;
(2)不管
怎么变化,都有A,
,
,
四点共圆,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf3c28abd6fe057aeca669199a6eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/a3b8dfe6603f4e98e8143ced71b26391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761d73623dcfb06f436844101786d71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)不管
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/8112f9185c7d48b015d9cd0525616b31.png)
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2021-06-21更新
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1267次组卷
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6卷引用:福建省福州市2021届高三高考考前模拟卷数学试题
福建省福州市2021届高三高考考前模拟卷数学试题湖南师范大学附属中学2021届高三下学期二模数学试题(已下线)第46讲 解析几何中的四点共圆问题-2022年新高考数学二轮专题突破精练(已下线)专题38 圆锥曲线中的圆问题-2(已下线)第五篇 向量与几何 专题10 圆锥曲线中的四点共圆问题 微点1 圆锥曲线中的四点共圆问题(一)(已下线)专题04 圆锥曲线经典题型全归纳(3)
名校
10 . 已知椭圆
的离心率为
,点
分别为其下顶点和右焦点,坐标原点为
,且
的面积为
.
的方程;
(2)是否存在直线
,使得
与椭圆
相交于
两点,且点
恰为
的垂心?若存在,求直线
的方程,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14aeac55d519010de23642ac22cfb0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)是否存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b86b8bf99386fc939c9c12b1355ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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5卷引用:福建省厦门外国语学校2021届高三5月高考适应性考试数学试题
福建省厦门外国语学校2021届高三5月高考适应性考试数学试题河南省洛阳市2021届高三二模数学(理)试题(已下线)NO.4 练悟专区——解答题突破练-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)(已下线)专题24 圆锥曲线中的存在性、探索性问题 微点1 圆锥曲线中的存在性问题辽宁省沈阳市第一二〇中学2023-2024学年高三第十次质量监测(最后一卷)数学试题