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1 . 已知
,且
,
,若方程
表示焦点在
轴上的椭圆,则这样的椭圆共有________ 个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6104538fb9b39de1913f538eaed7e077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d34afba5f43d301946429980327d3be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9b6ad6f6fce0c84edfbc7b9802e3d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1542c48f287494f0c5f70a5c9eb6bfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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2 . 我们通常把圆、椭圆、抛物线、双曲线统称为圆锥曲线.通过普通高中课程实验教科书《数学》2-1第二章《圆锥曲线与方程》的章头引言我们知道,用一个垂直于圆锥的轴的平面去截圆锥,截口曲线(截面与圆锥侧面的交线)是一个圆.实际上,设圆锥母线与轴所成角为
,不过圆锥顶点的截面与轴所成角为θ.则当
,截口曲线为圆,当
时,截口曲线为椭圆;当
时,截口曲线为双曲线;当
时,截口曲线为抛物线.则在长方体
中,
,
,点P在平面ABCD内,下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ad7d1e3fad77908415415d6b2a90f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051962073bb8d9fa55943300dfd2fa77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c1cfef1a4ccd3baa3bfc86e6c084f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f5d2e8186f0173d7862b1d39fb3dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
A.若点P到直线![]() ![]() |
B.若点P到直线![]() ![]() |
C.若![]() |
D.若![]() |
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3 . 已知椭圆
的左、右焦点分别为
,点
,
在
上,且满足
,
,则
的离心率为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475a3fdc7b27d5ffa8c864dc478903d4.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888465c45bb120ff2aa979006c87eb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79e4292aade9d5ed1d7b40e7e766740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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4 . 设椭圆
的左、右焦点分别为
,直线
交椭圆
于点
,
,若
的周长的最大值为16,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7215420e2e75a8a4f718c16646bbb23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4147f37263dc5cdebcf9d53b758977dc.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/47ff8a5886e42095da57422c8777c10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 已知点P在椭圆C:
上,C的左焦点为F,若线段
的中点在以原点O为圆心,
为半径的圆上,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60e42d256056bb6f6bb4434d27a49b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba4cc27b9d67bbe15f458cf0417a35d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a4a8c1a4a82bba944bfec5b1954417.png)
A.5 | B.6 | C.7 | D.8 |
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6 . 若
为椭圆
:
上一点,
,
为
的两个焦点,且
,则
( )
![](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/2a2319264f2b722c45c3f0204247799b.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1accaa97c379475f35e61f30d3b64fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1565358ed95afa71757c1d7d1fd2ea.png)
A.![]() | B.![]() | C.![]() | D.5 |
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7 . 若复数
满足
,则复数
在复平面内所对应点的轨迹是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa2e6104b95e89a613f2debf6e3d91a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
A.椭圆 | B.双曲线 | C.圆 | D.线段 |
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解题方法
8 . 已知
分别是椭圆
的左、右焦点,
是
上一点.若
,
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/0857c5a214d495ba7cdd52edd0636897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10db4b7331cf660f42164e2c6330e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知椭圆
的左、右焦点分别为F1,F2,点A,B是椭圆C上异于长轴端点的两点,且满足
,若
,则λ=( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1ee3b19b315b03efd44ff9c56ff5cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8174c73ce27865ba2ec48d337be275.png)
A.5 | B.4 | C.3 | D.2 |
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2024-03-13更新
|
398次组卷
|
2卷引用:广东省肇庆市封开县江口中学2024届高三下学期第一次月考数学试题
10 . 如图,设
、
分别是椭圆
的左、右焦点,点P是以
为直径的圆与椭圆在第一象限内的一个交点,延长
与椭圆交于点Q,若
,则直线
的斜率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/de070d62-e247-4153-bfb6-64090bf8daad.png?resizew=196)
![](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/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f9bbac0569459c119333eb54638496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/de070d62-e247-4153-bfb6-64090bf8daad.png?resizew=196)
A.![]() | B.![]() | C.![]() | D.![]() |
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