名校
解题方法
1 . 如图,已知椭圆
的离心率为
,点
在
上.
(1)求
的方程;
(2)设点
关于原点
对称点为
为
上异于
的动点,直线
分别交
轴于
两点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253bfd4a02407a65c97c811f7c8118a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/07e39702-9a98-4458-9295-330715b5326a.png?resizew=162)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbdd498c29baff72302805b1044285db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb40dae2b0f4048d3fabff25e6cbe443.png)
您最近一年使用:0次
2024-02-23更新
|
297次组卷
|
2卷引用:江西省九江市2023-2024学年高二上学期期末考试数学试题
名校
解题方法
2 . 已知椭圆C:
的左、右焦点分别为
,
、
,
,点
在椭圆C上.
(1)求椭圆C的方程;
(2)过点
的动直线l与椭圆C交于不同的两点A,B.试问x轴上是否存在定点Q,使得x轴恰好平分
?若存在,求出定点Q的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768fef914945a6e28f1f41740951435c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1151e47dfad2fc7e7dff6ebc17f7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850807898e7f29cb655608441af4064d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58e766e83bea5517ea54065165fe60a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850807898e7f29cb655608441af4064d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b550e4f9cee5d018ceffe7c0eaab8405.png)
(1)求椭圆C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8387b687579c4d5152175c9d19e24232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c7bbe0ac1c88c9d35978a7184ba553.png)
您最近一年使用:0次
解题方法
3 . 已知椭圆
的左、右焦点分别为
,
,
上不同两点A,
满足
,当
时,
.
(1)求
的方程;
(2)设直线
,
交于点
,已知
的面积为1,求
与
的面积之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.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/5241b1031d541a5a9024de2b265b8121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79c7134cfcb1855f928c9def7a1df49.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b283e4d7375d770823775e4036c9f6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7f2b5b1e9ef7dd60486b550eb4cbec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ba9b58de88d84cf9eeb74c334846ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f4882e15707e5c55a68f2eafa51276.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
的离心率为
,且过点
,
分别为椭圆
的左右顶点,点
是椭圆
上异于
的动点,直线
与直线
分别交于
两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/79ddd271-dd56-4886-a77d-b9bb71da7514.png?resizew=174)
(1)求椭圆的方程
(2)求线段
的长度的最小值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269e3de2f365af371714d0f323ee2448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a345c0ab9bc098efa03e17ea556fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/11b141148d19998c842aee2e5b1de63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c86c60c1e2c03439a55ddfc9bd2a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/79ddd271-dd56-4886-a77d-b9bb71da7514.png?resizew=174)
(1)求椭圆的方程
(2)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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5 . 已知椭圆
的两个焦点分别为
,过
的直线
与
相交手
两点.当
平行
轴时,
.
(1)求
的方程;
(2)当
的内切圆面积取得最大值时,求
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e543bc509aaf7c7e8ed2bcc8f9729b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23466441f4e24ad94059af62c85e524e.png)
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee4e8dd17eb6d8e3486b860872f21a8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c07ebcbfacda073208d483c58e8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
解题方法
6 . 设椭圆
的左、右焦点分别为
,左右顶点分别为
,已知椭圆
过点
,且长轴长为6.
(1)求椭圆
的标准方程;
(2)点
是椭圆
上一点(
不与顶点重合),直线
交
轴于点
,且满足
,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46f04ec60daf12082dc3f1bf8d2e67b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500272f9f312e2bc0f32e4afc058db41.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1dcef1a2703561586b4bd8f946cd41a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e5e3b13572a141ae74bfb65c925f19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
您最近一年使用:0次
2024-02-12更新
|
629次组卷
|
2卷引用:天津市五所重点校2023-2024学年高三上学期期末质量联合测试数学试题
解题方法
7 . 已知椭圆
,点
为椭圆
的左顶点,若点
在椭圆
上,点
为椭圆上任意一点,则
面积的最大值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a304696b261e993dcaa4038627ac9bab.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/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
您最近一年使用:0次
解题方法
8 . 已知椭圆
:
,点
,
在
上.
(1)求椭圆
的方程;
(2)过点
作与x轴不垂直的直线
,与椭圆C交于不同的两点A,B,点D与点A关于x轴对称,直线
与
轴交于点Q,O为坐标原点、若
的面积为2,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25e326fdf9e5456f48e8a99a069f379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d817c58c563afcba53cd59c6450ad7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
解题方法
9 . 已知椭圆
经过点
,离心率为
.
(1)求椭圆
的方程;
(2)设过点
的直线
与椭圆
有两个不同的交点
(均不与点
重合),若以线段
为直径的圆恒过点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b312367cf51225ea3bfbee2103b0c30.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
10 . 已知椭圆
过
,
两点,直线
过点
,且交椭圆
于
,
两点,交
轴于点
,
,
.记
的面积为
.
(1)求椭圆
的标准方程.
(2)证明:
为定值.
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84114a39cd1c55b43da8366588101842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b23b0b900e094d9bd641305c5e99110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dda128fd8bd88de4cdd76739788db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d35322b747f1e3f16bfa16235319ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e83d16535d2a8187bbd97507056559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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