名校
解题方法
1 . 已知双曲线
的两个焦点为
为
上一点,
,
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ed463bf16c78a4bbb9d3acff922afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff00fc29b9b9374935cf7bd256fb6234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb29fec0b08ce7a9fd357714bcf1a611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-03更新
|
521次组卷
|
5卷引用:吉林省长春市第二实验中学2023-2024学年高二下学期开学测试数学试题
名校
解题方法
2 . 已知椭圆
的左、右焦点分别为
,上顶点为
,离心率为
,若M,N为C上关于原点对称的两点,则( )
![](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/5cfba05dbe7c648be80649633f07b817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
A.C的标准方程为![]() |
B.![]() |
C.![]() |
D.四边形![]() ![]() |
您最近一年使用:0次
2024-03-01更新
|
310次组卷
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2卷引用:吉林省长春市第二实验中学2023-2024学年高二下学期开学测试数学试题
名校
解题方法
3 . 已知双曲线
,其中离心率为
,且过点
,求
(1)双曲线
的标准方程;
(2)若直线
与双曲线
交于不同的两点
,
,且
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b848246c11ebef783e4e50f35282774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09b0f43e2ab01bece17d3624d6ef9e9.png)
(1)双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb36455e34352b972eb1fc005100daa.png)
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4 . 如图,在多面体ABCDEF中,平面
平面ABCD,
是边长为2的等边三角形,四边形ABCD是菱形,且
,
,
.
平面ACF;
(2)在线段AE上是否存在点M,使平面MAD与平面MBC夹角的余弦值为
.若存在,请说明点M的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25eff69a4a0dc7a7ab183843303d333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6034301fc4110da89bdb0f46ad82ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
(2)在线段AE上是否存在点M,使平面MAD与平面MBC夹角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
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2024-02-04更新
|
406次组卷
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3卷引用:吉林省长春市朝阳区长春吉大附中实验学校2023-2024学年高二下学期4月月考数学试题
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解题方法
5 . 已知双曲线C:
的焦距为
,点
在C的渐近线上,则双曲线C的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530e5817131adf2c05b99ff18eb9060f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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6 . 如图,长方体
的底面
为正方形,
为
上一点.
(1)证明:
;
(2)若
平面
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419aee8a92d4b6ec81bf250c9ddb12d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/56634a11-d9cf-4f5e-81e7-5d74b1c1a8f1.png?resizew=114)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b6c68ad9b2e22725f3cbf7c1a3f8dc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adf679c5b5063388202ee10d28ee8c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
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2024-02-01更新
|
327次组卷
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4卷引用:吉林省通化市梅河口市第五中学2023-2024学年高二上学期期末数学试题
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7 . 已知双曲线
,焦点到渐近线距离为3,则其渐近线方程为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b7e47c0c6ca050e727a85bd1031c56.png)
您最近一年使用:0次
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解题方法
8 . 已知椭圆C:
,P为椭圆上一个动点,
为其左右焦点,当
垂直于
轴时,
,则下列选项正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd9d537bac0fd05b1b043f700aaa9cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb88c56652ad7b44873c7e1dfe355c5.png)
A.![]() |
B.![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() |
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9 . 已知曲线
,点
为平面内一动点,且与曲线
的焦点不重合.已知
关于曲线
的左焦点的对称点为
,关于右焦点的对称点为
,线段
的中点在双曲线
右支上,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb5d1183550c14659cf32bacfdaaf74.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/ac047e91852b91af639feec23a9598b2.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2735b4dead037d8ef258371bbd2654f.png)
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解题方法
10 . 设抛物线
的焦点为
,动直线
交抛物线于
,
两点,当直线
过焦点且
的中点
的横坐标为2时
.
(1)求抛物线
的方程;
(2)已知点
,当焦点为
为
的垂心时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0907a673d52825cd7df84b400972d4b9.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae02f139fdf785ced96e3980f1a6c57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-01-29更新
|
244次组卷
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2卷引用:吉林省通化市梅河口市第五中学2023-2024学年高二上学期期末数学试题