1 . 已知椭圆
:
的离心率为
,左顶点是
,左、右焦点分别是
,
,
是
在第一象限上的一点,直线
与
的另一个交点为
.若
,且
的周长为
,则直线
的斜率为_______ .
![](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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.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/8a7a2446c5d95b5835a541b105704aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/723377abda40d209ef7d7b2b44da1045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d2990bda1b57572f2292b4d65f1f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2024-01-23更新
|
86次组卷
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2卷引用:山东省临沂市第十九中学2023-2024学年高二上学期第五次质量调研考试数学试题
名校
解题方法
2 . 在平面直角坐标系
中,动圆
与圆
内切,且与圆
外切,记动圆
的圆心的轨迹为
.
(1)求轨迹
的方程;
(2)设
为坐标原点,过点
且与坐标轴不垂直的直线与轨迹
交于
两点.线段
上是否存在点
,使得
?若存在,求出
的取值范围;若不存在,说明理由;
(3)过点
且不垂直于
轴的直线与轨迹
交
两点,点
关于
轴的对称点为
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb1a1564d409a8d5908521e3432674f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43bb4c6bab49ddf60492153410604ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4c87b3f7044f650e3b6559df0493a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883f23ab75b490d6e9e03b8ff8b269c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f6aff6bc7b06b8656cf16970e30b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61372caa7455964777bb20c15b8e4a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
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2024-01-22更新
|
245次组卷
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2卷引用:山东省东营市2023-2024学年高二上学期1月期末质量监测数学试题
名校
3 . 椭圆
的离心率为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b24214f111f7c6d2b64e53ad970438b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.![]() | B.![]() | C.![]() | D.2 |
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2024-01-19更新
|
6746次组卷
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7卷引用:山东省济南市2023-2024学年高二上学期期末质量检测模拟数学试题
4 . 已知双曲线
的实轴长为8,且与椭圆
有公共焦点,则双曲线
的渐近线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd45c807c5b4278b917b69b4975cfb4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-01-15更新
|
887次组卷
|
3卷引用:山东省烟台市爱华高级中学2023-2024学年高二上学期期末模拟数学试题(二)A卷
山东省烟台市爱华高级中学2023-2024学年高二上学期期末模拟数学试题(二)A卷广东省佛山市2024届高三教学质量检测(一)数学试题(已下线)广东省佛山市2024届高三教学质量检测(一)数学试题变式题1-6
2024高三·全国·专题练习
名校
5 . “
”是“方程
表示椭圆”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cd410af83a4e172bd6b2847f2c3480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2346e88e70029b80556aec2d843f6db0.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
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解题方法
6 . 已知曲线C的方程为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2443fa7b959608e31eada4301f27a7bc.png)
A.当![]() |
B.当![]() ![]() |
C.当![]() |
D.存在实数m使得曲线C为双曲线,其离心率为![]() |
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解题方法
7 . 过椭圆
左焦点 F作x轴的垂线,交椭圆于 P,Q两点,A是椭圆与x轴正半轴的交点,且
,则该椭圆的离心率是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66305004cfecb91a482e7d0b515bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2409c92959a14648a1e6657654c230b4.png)
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2024-01-04更新
|
382次组卷
|
2卷引用:山东省潍坊市国开中学2023-2024学年高二下学期开学收心数学试题
8 . 已知
,当
为何值时:
(1)方程表示双曲线;
(2)表示焦点在
轴上的双曲线;
(3)表示椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303a8742c9c6fce46efffcc13160ab49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)方程表示双曲线;
(2)表示焦点在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)表示椭圆
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9 . (多选)已知曲线Γ:
(
),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8ac54e841cb79e68ee8071ebf809c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
A.Γ可能是等轴双曲线 |
B.若Γ表示焦点在y轴上的椭圆,则![]() |
C.Γ可能是半径为![]() |
D.若Γ表示焦点在x轴上的双曲线,则![]() |
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10 . 已知
,
分别为椭圆C:
的左、右焦点,P为C上一点,且
,O为坐标原点,则
的值为____________ .
![](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/c06ffc3051183ecdd0fa98799095bc13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d124b231bf2cd3746f35e6c68cd7178f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f645d4b09fba53f971172cd2602c691.png)
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