1 . 已知椭圆
过点
,且离心率为
.
(1)求椭圆C的标准方程;
(2)过椭圆C的右焦点F的直线l与椭圆相交于A,B两点,且
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23a03ca8f1729bfcadf513784817fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
(1)求椭圆C的标准方程;
(2)过椭圆C的右焦点F的直线l与椭圆相交于A,B两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d780f0607ef7e19996aa5274409cd103.png)
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名校
解题方法
2 . 已知椭圆
,四个点
,
,
,
中恰有三点在椭圆C上.
(1)求椭圆C的方程;
(2)设直线
与椭圆C相交于A,B两点.若直线
与直线
的斜率的和为
,判断直线l是否经过定点,若过定点,求出定点坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f669a1d6376f795f05b47eb7d8067c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7fbf46db1c38fdcefdfca8777a92875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea67de74c0d7a7c48df4329a625e9234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662c8324ff4c288337a2dbf78be863b4.png)
(1)求椭圆C的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e9f87f36df625060ebf7b0ede71b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3de68627f7f3d7f81b61bf743f311ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9019a986b3ba5fcefced99c566b5329c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
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2023-02-22更新
|
383次组卷
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3卷引用:内蒙古自治区赤峰市红山区2022-2023学年高二上学期期末数学理科试题
名校
解题方法
3 . 已知椭圆
经过点
,离心率为
.
(1)求椭圆
的方程;
(2)设经过右焦点
的两条互相垂直的直线分别与椭圆
相交于
,
两点和
,
两点.求四边形
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e454c7161999e2a67138869f59d319b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设经过右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/9c593ebdb2f1934a0cb56f8c44f454f8.png)
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2023-02-22更新
|
340次组卷
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3卷引用:四川省成都市2022-2023学年高二上学期期末调研考试数学(理科)试题
解题方法
4 . 已知椭圆
经过点
,离心率为
.
(1)求椭圆E的方程;
(2)设经过原点O的两条互相垂直的直线分别与椭圆E相交于A,B两点和C,D两点.求四边形ACBD的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e454c7161999e2a67138869f59d319b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆E的方程;
(2)设经过原点O的两条互相垂直的直线分别与椭圆E相交于A,B两点和C,D两点.求四边形ACBD的面积的最小值.
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解题方法
5 . 已知离心率为
的椭圆
过点
.
(1)求椭圆
的方程;
(2)设直线
与椭圆
交于不同的两点
,直线
分别交直线
于点
.当
面积为8时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee9d4ad39e56940f519bd3acc5e85ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad492d5033448d419df9c9b75a71894e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764ab1262baa09cd62fb6ddba39df2ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de9f075d2558b7dce0eb91148de84fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-02-22更新
|
447次组卷
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2卷引用:浙江省宁波市奉化区2022-2023学年高二上学期期末数学试题
名校
解题方法
6 . 求满足下列条件的曲线的标准方程:
(1)点
和点
的椭圆的标准方程;
(2)准线方程为
的抛物线的标准方程;
(3)求与双曲线
共渐近线,且过点
的双曲线的标准方程;
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc83347d419c0aae5b61c14f4164bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c19cbac5241a8ac00daffa8e1f910a5.png)
(2)准线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d0aa9412dd7caf42cc71520e282328.png)
(3)求与双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec547b073f963a99feadb396f8ed0a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cceff0e7d103475c3ba9a2712f373185.png)
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2023-02-21更新
|
171次组卷
|
2卷引用:宁夏回族自治区银川一中2022-2023学年高二上学期期末考试数学(文)试题
7 . 已知椭圆
(
)的离心率为
,且经过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1db47a746631df2abe52539a86aed1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/d5f89d39-1f71-4181-8028-38eedb2b3838.png?resizew=186)
(1)求椭圆
的方程;
(2)过
作两直线与抛物线
(m>0)相切,且分别与椭圆C交于P,Q两点,直线
,
的斜率分别为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
①求证:
为定值;
②试问直线
是否过定点,若是,求出定点坐标;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1db47a746631df2abe52539a86aed1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/d5f89d39-1f71-4181-8028-38eedb2b3838.png?resizew=186)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb573fb6f6f37fd615e35c4073c2919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1efe96e7776f1b5dfa92c295f8d97d.png)
②试问直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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2023-02-19更新
|
588次组卷
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3卷引用:辽宁省营口市2022-2023学年高三上学期期末数学试题
解题方法
8 . 已知椭圆
,离心率为
,点
在椭圆C上.
(1)求椭圆C的标准方程;
(2)记A是椭圆的左顶点,若直线l过点
且与椭圆C交于M,N两点(M,N与A均不重合),设直线AM,AN的斜率分别是
.试问
是否为定值?若是,求出定值;若不是,请说明理由.
![](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/bfc2210a7e09298897f6585ad08a70d3.png)
(1)求椭圆C的标准方程;
(2)记A是椭圆的左顶点,若直线l过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62ec9eb13c5cfca501ff84357595755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa0e5e0c2447e94026292646458952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
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22-23高二上·陕西宝鸡·期末
名校
解题方法
9 . 已知椭圆
的两焦点分别为
,且经过点
.
(1)求椭圆
的方程;
(2)设过椭圆的右焦点
且斜率为
的直线
交椭圆
于
两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ba951ce58ff7fb59c57e2d349fdc4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4a4aef3d4c96d68144715b3011eff1d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过椭圆的右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdc02f00cf00a6dfd88b53a90f1f7a4.png)
您最近一年使用:0次
2023-02-19更新
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531次组卷
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3卷引用:陕西省宝鸡市金台区2022-2023学年高二上学期期末理科数学试题
(已下线)陕西省宝鸡市金台区2022-2023学年高二上学期期末理科数学试题上海师范大学附属中学2022-2023学年高二下学期3月第二次月考数学试题江西省景德镇市乐平中学2023-2024学年高二上学期11月期中考试数学试题
名校
解题方法
10 . 已知椭圆
过点
,且离心率为
.
(1)求椭圆C的标准方程;
(2)直线
与曲线C交于M,N两点,O为原点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831cb11f50216541ff9a5c61f6f02749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)求椭圆C的标准方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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2023-02-18更新
|
453次组卷
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2卷引用:河北省沧州市2022-2023学年高二上学期期末数学试题