解题方法
1 . 已知椭圆
过点
分别为椭圆
的左、右焦点,且焦距为2.
(1)求椭圆
的方程;
(2)若不与坐标轴平行的直线
与椭圆相切于点
为坐标原点,求直线
与直线
的斜率之积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61e5d9b3ec8ad87bcdae145936d8051.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若不与坐标轴平行的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8255e035cfd3c2e84f10b236b6fd97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
解题方法
2 . 已知椭圆
的长轴长为
,且点
在椭圆
上.
(1)求椭圆
的方程.
(2)设
为坐标原点,过点
的直线
(斜率不为0)交椭圆
于不同的两点
(异于点
),直线
分别与直线
交于
两点,
的中点为
,是否存在实数
,使直线
的斜率为定值?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.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
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248ef83c35123d95c27a99abacde8d94.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2c46f50628332b4995b2435ef0e181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023-01-06更新
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3卷引用:河北省衡水市第十三中学2023届高三上学期质检(三)数学试题
3 . 已知椭圆C的右焦点与抛物线E:
的焦点F重合,且椭圆C的离心率为
.
(1)求椭圆C的标准方程.
(2)过点F的直线l交椭圆C于M,N两点,交抛物线E于P,Q两点,是否存在实数
,使得
为定值?若存在,求出这个定值和λ的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆C的标准方程.
(2)过点F的直线l交椭圆C于M,N两点,交抛物线E于P,Q两点,是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adeefb0f83cf0c5440cffb53d2ec0be1.png)
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2023-01-03更新
|
448次组卷
|
3卷引用:河北省部分学校2023届高三上学期期末数学试题
河北省部分学校2023届高三上学期期末数学试题吉林省松原市前郭尔罗斯蒙古族自治县第五中学2022-2023学年高三上学期期末考试数学试题(已下线)重难点突破06 弦长问题及长度和、差、商、积问题(七大题型)-2
解题方法
4 . 设椭圆E:
(
)的左、右焦点分别为
,
,点
在椭圆E上.
(1)求椭圆E的方程;
(2)设点T在直线
上,过T的两条直线分别交E于A,B两点和P,Q两点,且
,求直线
的斜率与直线
的斜率之和.
![](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/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93942c01c84441f20e269d9173c4ec11.png)
(1)求椭圆E的方程;
(2)设点T在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79f9972cd4f14ecfcea79f005800fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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|
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4卷引用:河北省保定市2023届高三上学期期末数学试题
河北省保定市2023届高三上学期期末数学试题江苏省南通市2022-2023学年高三上学期12月调研测试数学试题(已下线)北京市海淀区2023届高三上学期期末练习数学试题变式题16-21(已下线)第五篇 向量与几何 专题5 调和点列 微点4 调和点列综合训练
名校
5 . 已知中心为坐标原点,焦点在坐标轴上的椭圆
经过点
,
.
(1)求
的方程;
(2)已知点
,直线
与
交于
两点,且直线
的斜率之和为
,证明:点
在一条定抛物线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94718313450e8a66d1fd47728891375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c59b8c8470f9eb1d2686f5287991b59.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b671cdde6baf9ab577330696ca8ff121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4d9dc481eb068489c6fb35d47aadac.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/342ba1917a6b854ad111a3e6f5514934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808426112792e9a80a06f611b60827a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5445b4183917494ad8aa1731073dd1d5.png)
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|
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5卷引用:河北省定兴中学等校2022-2023学年高二上学期12月联考数学试题
6 . 已知椭圆
:
的左右焦点分别为
,
,且焦距为2,点
为椭圆
上的动点(异于椭圆的左、右顶点),
.
(1)证明:
;
(2)当
,
,过椭圆
左焦点
的直线
与椭圆交于两点
,在
轴上是否存在点
,使得
为定值?若存在,求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa4ae8d7537feb98c7de50302705609.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8483a96fde0543e18d383ed3ecd321.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210020e91dbd088c72734d3f2fe58c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46bf4629f39c248a055fb070de8b61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7787dfab61ed9830b531da365e592bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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名校
解题方法
7 . 已知椭圆的中心在原点,焦点在
轴上,离心率为
,且过点
.
(1)求椭圆的标准方程;
(2)倾斜角为
的直线
过椭圆的右焦点
交椭圆于
、
两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
(1)求椭圆的标准方程;
(2)倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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2022-11-03更新
|
660次组卷
|
3卷引用:河北省邢台市六校联考2022-2023学年高二上学期期中数学试题
解题方法
8 . 已知椭圆
的左、右焦点分别为
,上、顶点分别为
的面积为
,四边形
的四条边的平方和为16.
(1)求椭圆
的方程;
(2)若
,斜率为
的直线
交椭圆
于
两点,且线段
的中点
在直线
上,求证:线段
的垂直平分线与圆
恒有两个交点.
![](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/6907ce7126d4fa4526f051968823a477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d88cb57a0ad6352956292e1b5f625c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a6f362a7f8f972d6b329a882e940d1.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f766a9c61e8c4346ebc3be82f7d59c8.png)
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2022-09-14更新
|
1027次组卷
|
3卷引用:河北省邯郸市2023届高三上学期摸底数学试题
河北省邯郸市2023届高三上学期摸底数学试题(已下线)3.3(附加3)圆锥曲线定点与定值问题-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)湖南省衡阳市衡阳县2022-2023学年高二上学期期末数学试题
名校
解题方法
9 . 已知椭圆
的离心率为
,且C的左、右焦点与短轴的两个端点构成的四边形的面积为
.
(1)求椭圆C的方程;
(2)若直线
与x轴交于点M,与椭圆C交于P,Q两点,过点P与x轴垂直的直线与椭圆C的另一个交点为N,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a0e851643a5d2bb55f1884fe0c6714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6093eebca8f3ff82ce9298feb197e955.png)
(1)求椭圆C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/399980676af7789fb9a91c7fcdeb90d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
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2022-09-06更新
|
1038次组卷
|
4卷引用:河北省秦皇岛市部分学校2023届高三上学期开学摸底数学试题
河北省秦皇岛市部分学校2023届高三上学期开学摸底数学试题河北省廊坊市三河市第三中学2023届高三上学期第一次段考数学试题(已下线)专题30 圆锥曲线三角形面积与四边形面积题型全归类-1吉林省长春市第二中学2022-2023学年高三上学期第一次调研测试数学试题
名校
解题方法
10 . 已知椭圆C:
(
)的左、右焦点分别为
,
,过
的直线l与椭圆C相交于A,B两点,直线l的倾斜角为45°,
到直线l的距离为
.
(1)求椭圆C的焦距;
(2)若
,求椭圆C的方程.
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(1)求椭圆C的焦距;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a8ce713e8c40e21841ee757bb03e4b.png)
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2022-07-08更新
|
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12卷引用:河北省邢台市2021-2022学年高二下学期期末数学试题
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