解题方法
1 . 已知椭圆
:
的右焦点为
,离心率为
.
(1)求
的方程.
(2)若
,
为
上的两个动点,
,
两点的纵坐标的乘积大于0,
,
,且
.证明:直线
过定点.
![](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/5c7b07ace87ed58fdc1f1bc78a04aeda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69d166677557cadb3da32b4a7e152e3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad3a4d8eb0a4f3dd417124a19f60066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343a7ab6571ec674d8ec3dd5492fccaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4f96905656ca8f1849ab44f804e5ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2023-11-13更新
|
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|
3卷引用:河北省邯郸市六校联盟2023-2024学年高二上学期期中数学试题
名校
解题方法
2 . 已知椭圆
的离心率为
,且过点
.
(1)求椭圆C的方程;
(2)若椭圆C的上顶点为P,过P的两条直线
,
分别与C交于异于点P的A,B两点,若直线
,
的斜率之和为
,试判断直线
是否过定点?若是,求出该定点;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2fc66af1e6967e988c9670ca8ceeee.png)
(1)求椭圆C的方程;
(2)若椭圆C的上顶点为P,过P的两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2023-11-09更新
|
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|
4卷引用:河北省邯郸市永年区第二中学等校2023-2024学年高二上学期期中联考数学试题
解题方法
3 . 已知椭圆
的离心率为
.
(1)求数列
的通项公式;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a8be3dec4ec0c40f7821307c545bf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647020b0a1c11eaa91eb2b4ed9f2dd78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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解题方法
4 . 已知椭圆C:
的左、右焦点分别为
,
,P是C上任意一点(异于左右顶点),O为坐标原点,M,N分别为线段
,
的中点,若四边形PMON的周长为6,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f54caf7dd87fbb2866908f6baaf88a.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/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
A.C的长轴长为3 | B.C的离心率为![]() |
C.![]() | D.![]() |
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名校
解题方法
5 . 如图,
,
是双曲线
:
与椭圆
的公共焦点,点
是
,
在第一象限内的公共点,设
方程为
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/16/b82d5169-c2a3-4a4e-b3f8-8b40c73be131.png?resizew=203)
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c477e5ade921ffa8377c4719319380ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de280ccf8124b26fbbac81ea62646e35.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/16/b82d5169-c2a3-4a4e-b3f8-8b40c73be131.png?resizew=203)
A.![]() |
B.![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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|
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5卷引用:河北省邯郸市永年区第二中学2023-2024学年高二上学期12月月考数学试题
名校
6 . 已知椭圆
的左,右顶点分别为A,B,且椭圆C的离心率为
,点P是椭圆C上的一点,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4706acbdca5d7c24ea284ae052daad.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c29c3bfdae2d4fbe8a8deaa572a2e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed9041fe53ac45ac131ec97216efc527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4706acbdca5d7c24ea284ae052daad.png)
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3卷引用:河北省邯郸市第十中学2022-2023学年高二上学期期末数学试题
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7 . 历史上第一位研究圆锥曲线的数学家是梅纳库莫斯(公元前375年-325年),大约100年后,阿波罗尼斯更详尽、系统地研究了圆锥曲线,并且他还进一步研究了这些圆锥曲线的光学性质.如图甲,从椭圆的一个焦点出发的光线或声波,经椭圆反射后,反射光线经过椭圆的另一个焦点,其中法线
表示与椭圆
的切线垂直且过相应切点的直线,如图乙,椭圆
的中心在坐标原点,
分别为其左、右焦点,直线
与椭圆
相切于点
(点
在第一象限),过点
且与切线
垂直的法线
与
轴交于点
,若直线
的斜率为
,
,则椭圆
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9db9373e74ecf5d63ad98afe66aa4ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a10d23ff4ff1be567d781d7624a663c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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7卷引用:河北省邯郸市涉县第一中学2023届高三上学期期中数学试题
名校
解题方法
8 . 已知椭圆
的左、右焦点分别是
,若椭圆C的离心率
,则称椭圆C为“黄金椭圆”.O为坐标原点,P为椭圆C上一点,A和B分别为椭圆C的上顶点和右顶点,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f9772b3a117674e43222976a5dc816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3add10627e4dd860cef0e0b8c035ae74.png)
A.a,b,c成等比数列 | B.![]() |
C.![]() | D.若![]() ![]() |
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7卷引用:河北省邯郸市魏县第五中学2022-2023学年高二下学期开学返校数学试题
解题方法
9 . 已知点
,
和直线
.
(1)若
是直线
上一个动点,求
的最小值;
(2)若椭圆
以
为焦点且与直线
有公共点,求椭圆
的离心率的最大值.
![](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/3cc13f1877a59f1cedcc8eb9c5ea23a2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d46e3ac39fe24c845b379cdf5df402.png)
(2)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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解题方法
10 . 设椭圆
的左右焦点为
,
,
是
上的动点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.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)
A.离心率![]() |
B.![]() ![]() |
C.以线段![]() ![]() |
D.![]() |
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8卷引用:河北省邯郸市大名县第一中学2022届高三上学期强化训练(三)数学试题
河北省邯郸市大名县第一中学2022届高三上学期强化训练(三)数学试题江苏省南京市江宁区2020-2021学年高二上学期期末数学试题江苏省无锡市南菁高级中学2020-2021学年高二(强化班)上学期10月第一次阶段性考试数学试题广东省深圳市北京师范大学南山附属学校2021-2022学年高二上学期期中数学试题黑龙江省大庆中学2021-2022学年高二上学期期中数学试题重庆市天星桥中学2021-2022学年高二上学期第二次月考数学试题(已下线)第3章 圆锥曲线与方程 综合测试-【暑假自学课】2023年新高二数学暑假精品课(苏教版2019必修第一册)辽宁省鞍山市2023-2024学年高二上学期期中数学试题