名校
1 . 已知椭圆
的焦点在
轴上,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8106feaf0b7b67c1608639de851c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-18更新
|
663次组卷
|
3卷引用:北京市丰台区2023-2024学年高二上学期期末练习数学试卷
北京市丰台区2023-2024学年高二上学期期末练习数学试卷北京市门头沟区大峪中学2023-2024学年高二下学期开学考试数学试题(已下线)3.1.1 椭圆及其标准方程【第一练】“上好三节课,做好三套题“高中数学素养晋级之路
名校
2 . 已知
是双曲线
与椭圆
的左、右公共焦点,
是
在第一象限内的公共点,若
,则
的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a015affdb6a83fad856f4429c3c93a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a1a44d3500ea01822960d8ac64b748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-18更新
|
311次组卷
|
2卷引用:北京市大兴区2023-2024学年高二上学期期末检测数学试题
名校
解题方法
3 . 画法几何的创始人法国数学家加斯帕尔
蒙日发现:与椭圆相切的两条垂直切线的交点的轨迹是以椭圆中心为圆心的圆,我们通常把这个圆称为该椭圆的蒙日圆.已知椭圆
的离心率为
分别为椭圆的左、右焦点,
为椭圆上两个动点.直线
的方程为
.给出下列四个结论:
①
的蒙日圆的方程为
;
②在直线
上存在点
,椭圆
上存在
,使得
;
③记点
到直线
的距离为
,则
的最小值为
;
④若矩形
的四条边均与
相切,则矩形
面积的最大值为
.
其中所有正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97ec04a1aa7ac6fce72d589864940a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02904676fe59cd21f036b222273b8db.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/426725e54032dce0135c0cb184264602.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050973e046bf8aef978e0739bca3db98.png)
②在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
③记点
![](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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35929c347f939fbfe8773b8b3ee2fa31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bff8399dc513b553529ef15f26f79b8.png)
④若矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a315e4b5963127bf8550cde03ca1966d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a315e4b5963127bf8550cde03ca1966d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e715c40ab558d10904766dc3f58010ef.png)
其中所有正确结论的序号为
您最近一年使用:0次
2024-01-18更新
|
291次组卷
|
3卷引用:北京市大兴区2023-2024学年高二上学期期末检测数学试题
北京市大兴区2023-2024学年高二上学期期末检测数学试题北京市八一学校2023-2024学年高三下学期开学摸底考试数学试题(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
名校
4 . 抛物线
的焦点坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0261104a7c308433a0c0508ff20ea29a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-18更新
|
352次组卷
|
2卷引用:北京市第九中学2023-2024学年中高二下学期开学考试数学试题
名校
5 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,求函数
的单调递增区间;
(3)若函数
在区间
上只有一个极值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9023462cbf98e1a934896520bfcda3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-01-17更新
|
1548次组卷
|
4卷引用:北京市房山区2024届高三上学期期末数学试题
北京市房山区2024届高三上学期期末数学试题北京市东直门中学2024届高三下学期开学检测数学试题(已下线)艺体生新高考新结构全真模拟4(已下线)热点2-5 导数的应用-单调性与极值(8题型+满分技巧+限时检测)
名校
6 . 已知双曲线
与椭圆
有公共焦点,且左、右焦点分别为
,
,这两条曲线在第一象限的交点为
,
是以
为底边的等腰三角形,则双曲线
的标准方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63496aab640348ffc3769ab4b53bcf9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-01-17更新
|
335次组卷
|
3卷引用:北京市房山区2023-2024学年高二上学期期末考试数学试卷
北京市房山区2023-2024学年高二上学期期末考试数学试卷北京市门头沟区大峪中学2023-2024学年高二下学期开学考试数学试题(已下线)3.2.2 双曲线的简单几何性质【第三练】“上好三节课,做好三套题“高中数学素养晋级之路
名校
解题方法
7 . 已知椭圆C:
(
)的一个焦点为
,一个顶点为
.
(1)求椭圆
的方程和离心率;
(2)已知直线
与椭圆
相切于点
,直线
交
轴于点
,
为坐标原点,
,求
的面积.
![](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/6402773afa7bb94c129317c16ef85f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0913f2ab13b39b1dae508b352a542d5.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9531f1b05a0b88af18596eedff7ced53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
2024-01-17更新
|
269次组卷
|
2卷引用:北京市房山区2023-2024学年高二上学期期末考试数学试卷
名校
解题方法
8 . 已知直线
与抛物线
相交于
两点.
(1)写出抛物线
的焦点坐标和准线方程;
(2)求弦长
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1794ac1aa451cda13537d610a2268bba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)写出抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
2024-01-17更新
|
354次组卷
|
2卷引用:北京市房山区2023-2024学年高二上学期期末考试数学试卷
2024高三·全国·专题练习
名校
解题方法
9 . 已知双曲线
的右焦点为
,则该双曲线的离心率等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0c83d2ece60c6f21309099472c9186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c3a2f5b0702ea9fbb9dc8904579737.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
10 . 已知椭圆
的右焦点为F,点P是椭圆与x轴正半轴的交点,点Q是椭圆与y轴正半轴的交点,且
,
.直线l过圆
的圆心,并与椭圆相交于A,B两点,过点A作圆O的一条切线,与椭圆的另一个交点为C,且
.
(1)求椭圆的方程;
(2)求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b5cee464e48a906ab59e4d678c87946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de75fbe52dd9ad026997cafbb50cd6f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07cb57d9eb1a433319f8efc6fb363660.png)
(1)求椭圆的方程;
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
2024-01-16更新
|
305次组卷
|
3卷引用:北京市西城区北京师范大学附属中学2023-2024学年高三下学期开学测试数学试题