名校
解题方法
1 . 已知椭圆
,椭圆
与椭圆
具有相同的离心率,且经过点
.
(1)求
的标准方程;
(2)若
的焦点在x轴上,
为
上一点,A、B两点在
上,且线段PA、PB的中点都在
上.
(i)当点P运动时,
的面积是否为定值?若是,求出该定值;若不是,请说理由;
(ii)记
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86022205a7487439dd8d0897cd3bf19.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(i)当点P运动时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd07c11236a5d229135c88e66c13778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
解题方法
2 . 已知椭圆
的短轴长等于焦距,且过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
(1)求椭圆
的方程;
(2)
为直线
上一动点,记椭圆
的上下顶点为
,直线
分别交椭圆
于点
,当
与
的面积之比为
时,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f207bd173cac9d3fcabcae4687557a1b.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/790ef3382b1c731f2885eecfd92c2a86.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/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2024-04-01更新
|
407次组卷
|
2卷引用:陕西省西安市长安区2024届高三下学期第一模拟考试理科数学试卷
名校
解题方法
3 . 如图,已知椭圆
经过点
,离心率
.
的标准方程;
(2)椭圆
上任意点
轴上一点
,若
的最小值为
,求实数
的取值范围;
(3)设
是经过右焦点
的任一弦(不经过点
),直线
与直线
相交于点
,记
的斜率分别为
,求证:
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04147e15b00989da8277da4422f8b443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81828dcd00a71cf376e8003488886bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f959ea4e8be882517c570b7bd7ad0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce0dbfbaede9bcbc415a105e36688e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c58b986bea8854118adc80af4437ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166a8e1bcb93423697696e2ba0409fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf3a71536f4f45cd75732e8b48592eb.png)
您最近一年使用:0次
2024-03-29更新
|
474次组卷
|
4卷引用:湖北省武汉市第二中学2023-2024学年高三下学期模拟考试(最后一卷)数学试卷
湖北省武汉市第二中学2023-2024学年高三下学期模拟考试(最后一卷)数学试卷上海市向明中学2023-2024学年高二下学期3月月考数学试题上海市松江二中2023-2024学年高二下学期期中数学试卷(已下线)专题02圆锥曲线全章复习攻略--高二期末考点大串讲(沪教版2020选修一)
解题方法
4 . 在平面直角坐标系
中,重新定义两点
之间的“距离”为
,我们把到两定点
的“距离”之和为常数
的点的轨迹叫“椭圆”.
(1)求“椭圆”的方程;
(2)根据“椭圆”的方程,研究“椭圆”的范围、对称性,并说明理由;
(3)设
,作出“椭圆”的图形,设此“椭圆”的外接椭圆为
的左顶点为
,过
作直线交
于
两点,
的外心为
,求证:直线
与
的斜率之积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9859b2a9747b7a9da0b87624231e5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de32f743ea0cf45f9822dd603be212d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd95e24f73f48167eb193951bd4fa7fb.png)
(1)求“椭圆”的方程;
(2)根据“椭圆”的方程,研究“椭圆”的范围、对称性,并说明理由;
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715c3978c454777672e14a72298317a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0dd7df0a96857b265fbbf745873ace9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2024-03-22更新
|
946次组卷
|
3卷引用:新疆乌鲁木齐地区2024届高三第二次质量监测数学试题
解题方法
5 . 已知椭圆
过
两点.
(1)求椭圆C的方程;
(2)已知过椭圆C的左顶点A的两条相互垂直的直线分别交椭圆C于P,Q两点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae885b367564ebb4806b86fa9c54902.png)
(1)求椭圆C的方程;
(2)已知过椭圆C的左顶点A的两条相互垂直的直线分别交椭圆C于P,Q两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
您最近一年使用:0次
2024-02-13更新
|
459次组卷
|
2卷引用:陕西省2024届高三教学质量检测(一)文科数学试题
6 . 已知椭圆
的焦点坐标
,且过点
.
(1)求椭圆
的标准方程;
(2)直线
与椭圆
交于
,
两点,且
,
关于原点的对称点分别为
,
,若
是一个与
无关的常数,求此时的常数及四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe45bd9ad543a4974aeca26d6230061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667aea83f946c1af51168af3b41a470d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240f005b4078f4fde9cbc0d7e53d47eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
您最近一年使用:0次
2024-01-24更新
|
209次组卷
|
3卷引用:江西省上高二中2024届高三适应性考试数学试卷
江西省上高二中2024届高三适应性考试数学试卷贵州省铜仁市2023-2024学年高二上学期1月期末质量监测数学试题(已下线)湖北省武汉市(武汉六中)部分重点中学2024届高三第二次联考数学试题变式题17-22
2023·全国·模拟预测
名校
解题方法
7 . 已知椭圆C:
的两焦点分别为
,并且经过点
.
(1)求椭圆C的方程;
(2)过
的直线交椭圆C于A,B两点,设直线
与C的另一个交点分别为M,N,记直线AB,MN的倾斜角分别为
,当
取得最大值时,求直线AB的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5439f5ff9bd5deec0f0ef35c6f605b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34dda3fc71497fe1a7ef2f3d2c2a953.png)
(1)求椭圆C的方程;
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0068ae8bb3fb1c75a3843e590fb30607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd927b4b5a7875528c1b54aa4bb8b2dd.png)
您最近一年使用:0次
2024-01-02更新
|
442次组卷
|
6卷引用:2024年全国高考名校名师联席命制型数学信息卷(七)
(已下线)2024年全国高考名校名师联席命制型数学信息卷(七)(已下线)2024年全国高考名校名师联席命制数学(理)信息卷(四)(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(三)江西省上饶市玉山县第二中学2023-2024学年高二上学期12月月考数学试题四川省成都市石室中学2023-2024学年高二上学期期末综合复习数学试题(一)山东省菏泽市2024届高三上学期期末考试数学试题(B)
2023·全国·模拟预测
解题方法
8 . 已知椭圆
的中心为坐标原点,对称轴为
轴、
轴,且
的一个焦点为
,并过点
.
(1)求
的方程.
(2)设
,
为
的上、下顶点,
,
是椭圆
上不同于
,
的两个动点.若直线
与直线
交于点
,点
满足
轴,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5421a28dc3675ae20190d6090793246e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8fed79fefddfb7ad03ee8b4eefdc563.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06b75fb4e379ff3b99e68f40136cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1745c0828d4f0050bf672ae0552e29c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
9 . 设椭圆
过点
,且左焦点为
.
(1)求椭圆
的方程;
(2)
内接于椭圆
,过点
和点
的直线
与椭圆
的另一个交点为点
,与
交于点
,满足
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9b4a5f5334c153ddbefc763d8939ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486279e7ff9f2b76c2ce712f5dedcb9c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8115c09f801cf0bb02293baef7bf137.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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解题方法
10 . 已知椭圆
经过点
,过原点的直线与椭圆交于
,
两点,点
在椭圆上(异于
,
),且
.
(1)求椭圆的标准方程;
(2)若点
为直线
上的动点,过点
作椭圆的两条切线,切点分别为
,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af292f60c635d2bb4c38379c6bd04ac5.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/895dc3dc3a6606ff487a4c4863e18509.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/daa7a1a4ff471aac32bf53e95ff9de9a.png)
(1)求椭圆的标准方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/a51661406851152e02b52989910cbd27.png)
您最近一年使用:0次
2023-05-05更新
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6卷引用:河北省名校2023届高三5月模拟数学试题
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