1 . 已知椭圆
的离心率为
,直线
与该椭圆交于
两点,分别过
向
轴作垂线,若垂足恰为椭圆的两个焦点,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 若双曲线
的实轴长为
,焦距为
,右焦点为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
A.![]() ![]() ![]() | B.![]() ![]() |
C.![]() ![]() ![]() | D.过![]() ![]() |
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3 . 过抛物线C:
(
)的焦点F且垂直于y轴的直线与C交于A,B两点,若
.
(1)求抛物线的方程;
(2)设直线
与抛物线C交于P,Q两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
(1)求抛物线的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23fc11a3a7592c68b20f93bdde2ed3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
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4 . 已知抛物线
的焦点为
是
上的点,且
.
(1)求
的方程;
(2)已知直线
交
于
两点,且
的中点为
,求
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315ade6f1c078456b174d1fa56a65ca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23359c60aaf591f98b0ed48522f9c48a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf4212afb2cfabd73893af322539b18d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bb053c0c73bccec3ba5cb1d8c83fb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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|
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解题方法
5 . 已知直四棱柱的底面
是菱形,且
,
分别是侧棱
的中点.
(1)证明:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a46615f8a942d2b83f40a71ff96eef.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
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6 . 已知抛物线
,点
在
上,过点
的直线
与
相交于
两点,直线
的斜率分别为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8902bff3e60ecebdcd71bb2ee8bb97b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9380191d5128132ab5995d3f048d3539.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/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.![]() ![]() |
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解题方法
7 . 已知椭圆
经过点
和
.
(1)求
的方程;
(2)若点
(异于点
)是
上不同的两点,且
,证明直线
过定点,并求该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea8a480a2fe03293cb8303da8837d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32476e6bf0fed9c3d3f23ebfd40aa693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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名校
解题方法
8 . 在棱长为2的正方体
中,
分别为棱
的中点,
为线段
上的一个动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f30422880a52311e68cfe78ad6131e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c4f409aa1d8abb7fe8d781c3951de02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
A.三棱锥![]() |
B.存在点![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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解题方法
9 . 在三棱锥
中,
平面
分别是棱
的中点,
,则直线
与平面
所成角的正弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce54f18bbf2aa43bb76db15f3f2f526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8eea77d3780398d78a9b5bd61a65c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f128c87fd0414aea9aba7cfccd6ce99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 经过椭圆
的左焦点
的直线与椭圆交于A,B两点(非顶点),
为右焦点,则
的周长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e903ad9a2806998db8ed16283bec8568.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/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
A.![]() | B.![]() | C.![]() | D.4 |
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