名校
1 . 已知椭圆
:
的焦点为
,
,且过点
.
(1)求椭圆
的方程;
(2)设椭圆的上顶点为
,过点
作直线交椭圆于
,
两点,记直线
,
的斜率分别为
,
,试判断
是否为定值?若为定值,求出该定值;若不是定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13683e2ecf2164a0adbfdb9923d210a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e454c7161999e2a67138869f59d319b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设椭圆的上顶点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f9f734c03d04c21edefa08e0acc1fa.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/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd6a1d6fab318824426e52464a575e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18abc8b447e4a6ff19e6bd4a30cb7b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27276690bf29f1d2816803bc3cacdfb.png)
您最近一年使用:0次
2020-11-28更新
|
1661次组卷
|
5卷引用:黑龙江省2020-2021学年高二第一学期学业水平考试 数学(理)试题
2 . 已知
、
是椭圆
长轴的两个端点,
、
是椭圆上关于
轴对称的两点,直线
、
的斜率分别为
、
.若椭圆的离心率为
,则
的最小值为( )
![](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/7dd54b9df3402ad91e2d34c40efe0c7a.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8c2d0ed3cffe8f28425cccc85e38bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9691613aae1a69934d3e3d2d599f748.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
3 . 已知圆
上有一动点
,点
的坐标为
,四边形
为平行四边形,线段
的垂直平分线交
于点
.
(Ⅰ)求点
的轨迹
的方程;
(Ⅱ)过点
作直线与曲线
交于
两点,点
的坐标为
,直线
与
轴分别交于
两点,求证:线段
的中点为定点,并求出
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88305ca764fd5b2be73bfcd289fb71b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2535ae76ff638079c5344599e4e23d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55ecbc50ac24239f0e5d6d2ae182254d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9ce1ab633b923b3b06f5d12dfd51b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅰ)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb398137779190b35492d9f06d5fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bb36a6010056e8462b8f830d9d037a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7490886e2807c7b8a4fa57d99c4dc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e8acea56a9f17e6ef9bbce1633497f.png)
您最近一年使用:0次
2020-04-16更新
|
738次组卷
|
8卷引用:河南省天一大联考2021届高三下学期阶段性测试(六)数学(理科) 试题
2020高三·江苏·专题练习
4 . 已知椭圆E:
+
=1(a>b>0)的离心率为
,焦点到相应准线的距离为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/391632be-5af3-4ef3-a312-e146bb15b6b8.png?resizew=186)
(1) 求椭圆E的标准方程;
(2) 已知P(t,0)为椭圆E外一动点,过点P分别作直线l1和l2,直线l1和l2分别交椭圆E于点A,B和点C,D,且l1和l2的斜率分别为定值k1和k2,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7355be4fcbc3130a5951364a3be76d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5268413295580cfda0755ab458b36b64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/391632be-5af3-4ef3-a312-e146bb15b6b8.png?resizew=186)
(1) 求椭圆E的标准方程;
(2) 已知P(t,0)为椭圆E外一动点,过点P分别作直线l1和l2,直线l1和l2分别交椭圆E于点A,B和点C,D,且l1和l2的斜率分别为定值k1和k2,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2efd9f1d286d417d5596e4fa2b52a4.png)
您最近一年使用:0次
5 . 已知椭圆
,点
,点
满足
(其中
为坐标原点),点
在椭圆
上.
(1)求椭圆
的标准方程;
(2)设椭圆的右焦点为
,若不经过点
的直线
与椭圆
交于
两点.且与圆
相切.
的周长是否为定值?若是,求出定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a932be759af5806cc4d5cb06dba1669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0e5df6dc2c9feed64a2f3cdcbe8018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4cf40b6cf2051622c0a52e84710c138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设椭圆的右焦点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b5d43b29783d7b5498a9bf9150fe15.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/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33181b27b10690b4913595f8c1f46e.png)
您最近一年使用:0次
2020-03-13更新
|
466次组卷
|
3卷引用:2019届黑龙江省学业水平考试数学(文科)试卷
6 . 椭圆
的左、右顶点分别为
、
,点
为曲线
上异于
、
的一点,直线
、
的斜率分别为
、
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d82f6055983b8e9bb5a9cd8e09ebe5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d82f6055983b8e9bb5a9cd8e09ebe5.png)
您最近一年使用:0次
名校
7 . 已知椭圆
的离心率为
,且过点
,若点
在椭圆C上,则点
称为点M的一个“椭点”.
(1)求椭圆C的标准方程;
(2)若直线
与椭圆C相交于A,B两点,且A,B两点的“椭点”分别为P,Q,以PQ为直径的圆经过坐标原点,试判断
的面积是否为定值?若为定值,求出定值;若不为定值,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/3fe8530b8e246a9a5ec9fe3b9c347d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915805abfac8f498563f530b9f244592.png)
(1)求椭圆C的标准方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
2020-02-27更新
|
315次组卷
|
2卷引用:2018级山东师大附中第五次学分认定考试数学试题
解题方法
8 . 在平面直角坐标系
中,已知椭圆
的左、右焦点分别为
,且点
与椭圆C的上顶点构成边长为2的等边三角形.
![](https://img.xkw.com/dksih/QBM/2020/6/8/2480068559888384/2480296452120576/STEM/920490cef427499f84f0d64c8457a228.png?resizew=246)
(1)求椭圆C的方程;
(2)已知直线l与椭圆C相切于点P,且分别与直线
和直线
相交于点
.试判断
是否为定值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://img.xkw.com/dksih/QBM/2020/6/8/2480068559888384/2480296452120576/STEM/920490cef427499f84f0d64c8457a228.png?resizew=246)
(1)求椭圆C的方程;
(2)已知直线l与椭圆C相切于点P,且分别与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df51575d9a6b6c449c50d553c68ebb1.png)
您最近一年使用:0次
名校
解题方法
9 . 已知椭圆
(
)的离心率为
,长轴长为
,左、右焦点分别为F1,F2,上顶点为A.
(1)求椭圆的方程;
(2)若点P为椭圆上一点,且∠F1F2P=90°,求△F1F2P的面积;
(3)过点A作斜率为k1,k2的两条直线,分别交椭圆于D,E两点,若D,E两点关于原点对称,求k1k2的值.
![](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/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆的方程;
(2)若点P为椭圆上一点,且∠F1F2P=90°,求△F1F2P的面积;
(3)过点A作斜率为k1,k2的两条直线,分别交椭圆于D,E两点,若D,E两点关于原点对称,求k1k2的值.
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