1 . 已知在平面直角坐标系
中,椭圆
的右顶点为
,上顶点为
,
的面积为
,离心率
.
(1)求椭圆
的方程;
(2)若斜率为
的直线
与圆
相切,且
与椭圆
相交于
、
两点,若弦长
的取值范围为
,求斜率
的取值范围.
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b92075c4fff5c0a08fe4475fd29dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
2 . 已知在平面直角坐标系
中,椭圆
的右顶点为A,上顶点为B,
的面积为
,离心率
.
(1)求椭圆C的方程;
(2)若斜率为k的直线
与圆
相切,且l与椭圆C相交于
两点,若弦长
的取值范围为
,求
的取值范围.
![](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/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求椭圆C的方程;
(2)若斜率为k的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2ac18a8a2c5603d9588666978309e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b92075c4fff5c0a08fe4475fd29dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7db9b4ac9106bfaf32eba6ae265872b.png)
您最近一年使用:0次
3 . 过椭圆
的左焦点作直线和椭圆交于A、B两点,且
,则这样直线的条数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf679418512d6ad973531df808fd267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d7b490a6347e3dc15c2b559e8eb62f.png)
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
2023-06-01更新
|
362次组卷
|
4卷引用:北京名校2023届高三一轮总复习 第7章 解析几何 7.7 直线与椭圆的位置关系(1)
北京名校2023届高三一轮总复习 第7章 解析几何 7.7 直线与椭圆的位置关系(1)(已下线)专题3.3 直线与椭圆的位置关系【八大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)3.1.2 椭圆的简单几何性质(10大题型)精讲-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)(已下线)3.1.2 椭圆的几何性质(10大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)
4 . 已知直线
与椭圆
交于M、N两点,且
.求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd55f837e9c4e6bba1163ef13edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83a5ffb5d4720252b39dbafe82b5b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
解题方法
5 . 已知直线
与椭圆
在第二象限交于
两点,且
与
轴、
轴分别交于
两点,若
,
,则
的方程为 ______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee3f2b59cfb962db4f5e576b2f8a7e1.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d541d1d1d1d74c03c9d3c8db384fccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b0dfa6898f9560ab8a5e5905c1f81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
6 . 在平面直角坐标系
中,已知椭圆
:
与椭圆
:
,且椭圆
过椭圆
的焦点.过点
且不与坐标轴平行或重合的直线
与椭圆
交于
,
两点,与椭圆
交于
,
两点.
(1)求椭圆
的标准方程;
(2)若存在直线
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77bb900f8c975bf487cd57319d488938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f642cc82f9cb94f68265b4ec78f8c2.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/d2d466e7019fc215699264d18069b87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b29fa3fdb0b5df281c8a847c662b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-05-18更新
|
434次组卷
|
3卷引用:第09讲 拓展三:圆锥曲线的方程(弦长问题)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)
(已下线)第09讲 拓展三:圆锥曲线的方程(弦长问题)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)河北省保定市唐县第一中学2023届高三二模数学试题黑龙江省齐齐哈尔市实验中学2023届高三三模数学试题
名校
解题方法
7 . 在生活中,我们经常看到椭圆,比如放在太阳底下的篮球, 在地面上的影子就可能是一个椭圆. 已知影子椭圆
,C的上顶点为A,两个焦点为
,
,离心率为
.过
且垂直于
的直线与C交于D,E两点,
,则
的最小值是________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3b52d2dcf997ef34cd29141a2f90d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57b2fd43664357e735db4bba8fa6f32.png)
您最近一年使用:0次
2023-05-13更新
|
757次组卷
|
4卷引用:湖北省黄冈市浠水县第一中学2023届高三下学期5月高考仿真模拟数学试题
湖北省黄冈市浠水县第一中学2023届高三下学期5月高考仿真模拟数学试题(已下线)第02讲 3.1.2椭圆的简单几何性质(3)(已下线)第08讲 直线与圆锥曲线的位置关系(四大题型6个方向)(讲义)-2河北省石家庄市第二中学2023-2024学年高二上学期期末第一次模拟考数学试题
8 . 如图,直线
与椭圆
交于
、
两点,记
的面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/4e7a2376-e6de-4930-b825-2d2635e2c047.png?resizew=211)
(1)若线段
的中点为
,求此时直线
的方程;
(2)当
,
时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.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/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/4e7a2376-e6de-4930-b825-2d2635e2c047.png?resizew=211)
(1)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86630cdec59f9ec8f34e1995d3e54f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7288d0b18af1a4be7f8df09af45df1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-04-22更新
|
409次组卷
|
4卷引用:浙江省杭州市第四中学下沙校区2022-2023学年高二下学期期中数学试题
浙江省杭州市第四中学下沙校区2022-2023学年高二下学期期中数学试题四川省蓬溪中学校2022-2023学年高二下学期月考(理科)数学试题四川省蓬溪中学校2022-2023学年高二下学期月考(文科)数学试题(已下线)第04讲 拓展一:直线与椭圆的位置关系-【练透核心考点】2023-2024学年高二数学上学期重点题型方法与技巧(人教A版2019选择性必修第一册)
解题方法
9 . 已知椭圆
过点
和
,且
.
(1)求椭圆
的方程;
(2)过点
斜率为
的直线
交椭圆
于
,直线
分别交直线
于点
.若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e755804d23862a82d32bd7f901c23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4037561c629fd07503c6803e1eb62fb6.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bdfbae913ff7ff8caaefcaacf8c20ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c5f9ca221a6f845205864209fa4a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c7a6d1ca70f98927fa7d45b9fb7b34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/837fee3d3a6a1313ca120df3e98fd5cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-04-11更新
|
1695次组卷
|
5卷引用:北京市顺义区2023届高三一模数学试题
名校
解题方法
10 . 椭圆E的方程为
,短轴长为2,若斜率为
的直线与椭圆E交于
两点,且线段
的中点为
.
(1)求椭圆E的方程;
(2)若直线l:
与圆
相切,且与椭圆E交于M,N两点,且
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3fda5d92d4f2a23a5c84f0855d0501.png)
(1)求椭圆E的方程;
(2)若直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d86a6026abea99737de584cd5edc55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3834dd00dbca1d1ec6729ddbd8647b.png)
您最近一年使用:0次