解题方法
1 . 定义离心率是
的椭圆为“黄金椭圆”.已知椭圆
是“黄金椭圆”,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
______ .若“黄金椭圆”
的两个焦点分别为
,
,
为椭圆
上异于顶点的任意一点,点
是
的内心,连接
并延长交
于点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978311c18754ba498c1ee0dce2f89482.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d393bb07b7140905b85f550519de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114c0db91c76cfbe5924fb52fa30f970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddf5a506a90d09af01b81db43f17e93.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978311c18754ba498c1ee0dce2f89482.png)
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2 . 设椭圆
与双曲线
(其中
)的离心率分别为
,
,且直线
与双曲线的左、右两支各交于一点,下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a560f37921b2fd014c60c4f5b5266d0.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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解题方法
3 . 椭圆
的左焦点
关于直线
的对称点
在椭圆上,则椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0944c99f34ee41bea845303ed15a7d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a6de29ad2450563048057328e64a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知椭圆
的离心率为
,
,
,
,
,设P为椭圆C上一点
的面积的最大值为
.
(1)求椭圆C的方程;
(2)当P在第三象限,直线
与y轴交于点M,直线
与x轴交于点N,求证:四边形
的面积为定值.
![](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/b3160fc73f2a90ae4a1a97351ab2673b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9199b50dd0036be9b764c621d1d46f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87e24ea042ecf3f25150338e22b45b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1a9821a00b71f6b7d7a76d91b3f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374cdec65a41dc616f6f099551880d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
(1)求椭圆C的方程;
(2)当P在第三象限,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
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解题方法
5 . 已知椭圆
的左焦点为
,过原点
的直线
交椭圆于
,
两点,点
在第二象限,且
(如图),则椭圆的离心率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc653312ef32b1e98025b79963cc47d.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d8030884be606b9710f058cf49dd81a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/6af3fb0f-65ef-45ee-a96d-26e0441d4326.png?resizew=150)
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解题方法
6 . 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)
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2024-02-23更新
|
297次组卷
|
2卷引用:湖北省武汉市华中师大第一附中2023-2024学年高二下学期数学独立作业(一)
解题方法
7 . 已知椭圆C:
(
,
)右焦点为F,M,N是椭圆上关于原点对称的两点,且不在坐标轴上,线段FM、FN的中点分别为A,B,且
,则椭圆C的离心率可以为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1eb76fe74cba30f7cbcde349ba80da.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 已知椭圆
的离心率为
.直线
经过点
和椭圆
的上顶点,其斜率为
.
的标准方程;
(2)若直线
与椭圆
交于
、
两点,直线
与椭圆
的另一个交点为
,直线
与椭圆
的另一个交点为
.求证:当
变化时,直线
过定点.
![](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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf02334810fe35d00fe99d2945fbfbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861fe213ebc09184f67a05173ad3a941.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/20a541b81584a032f571159ea152c85a.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/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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解题方法
9 . 已知曲线
与y轴交于A,B两点,P是曲线C上异于A,B的点,若直线AP,BP斜率之积等于
,则C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c623fe58727acdd1fd4964b4947df4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03aa30b6d5bfcefb197cc2046479ed65.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-02-05更新
|
440次组卷
|
3卷引用:湖北省荆州市八县市区2023-2024学年高二上学期1月期末联合考试数学试题
湖北省荆州市八县市区2023-2024学年高二上学期1月期末联合考试数学试题河南省南阳市第一中学校2023-2024学年高二下学期开学考试数学试题(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)
解题方法
10 . 已知椭圆
的离心率
在椭圆上.
(1)求椭圆
的标准方程;
(2)已知动直线
(斜率存在)与椭圆相交于点
两点,且
的面积
,若
为线段
的中点.
点在
轴上投影为
,问:在
轴上是否存在两个定点
,使得
为定值,若存在求出
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bd04850467c1df65541e93912c167f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1731169574e86f63684590a8b8f67df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b397875f3272bf8bc0cc50c2cda53ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
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