名校
1 . 在正方体
中,
,
分别为
,
中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() ![]() |
D.平面![]() ![]() ![]() |
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2024-01-28更新
|
188次组卷
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2卷引用:辽宁省葫芦岛市2023-2024学年高二上学期1月普通高中学业质量监测考试数学试题
名校
2 . 已知双曲线C的方程为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58fa4a337f0b81b991fb32e8e6e3c0.png)
A.双曲线C的实轴长为6 |
B.双曲线C的渐近线方程为![]() |
C.双曲线C的焦点到渐近线的距离为4 |
D.双曲线C上的点到焦点距离的最小值为8 |
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2024-01-28更新
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493次组卷
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2卷引用:辽宁省大连市2023-2024学年高二上学期期末数学试题
解题方法
3 . 过点
的直线
与抛物线
交于不同两点A、B.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e5e815fc2bbf03d424b52fa920dd0e.png)
______ .(O为坐标原点)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e5e815fc2bbf03d424b52fa920dd0e.png)
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4 . 椭圆
的焦点坐标为 ______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c190e8bb81a4d26cf638ed246193cc9.png)
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5 . 已知
是椭圆
的左焦点,第一象限内的点
在
上,直线
与
轴交于点
为坐标原点,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3ceeab6bf04f0c65f43583b3661a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f4411b37e8ed03b1841906af3bf912f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7375a1fda8639f2d368c52c5bb9d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-26更新
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367次组卷
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3卷引用:辽宁省抚顺市六校协作体2023-2024学年高二上学期期末考试数学试题
名校
6 . 画法几何的创始人——法国数学家加斯帕尔•蒙日发现:在椭圆中,任意两条互相垂直的切线的交点都在同一个圆上,它的圆心是椭圆的中心,半径等于长、短半轴的平方和的算术平方根,我们通常把这个圆称为该椭圆的蒙日圆.已知椭圆
,则其蒙日圆方程为__________ ,若
为蒙日圆上一个动点,过点
作椭圆
的两条切线,与蒙日圆分别交于
、
两点,则
面积的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.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/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/2205cffebf8c4d5f81d15ed7b85c8936.png)
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解题方法
7 . 直三棱柱
中,
,则直线
与
夹角的余弦是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d643cd59b0a65b188b1142347263459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 在平面直角坐标系中,已知点
,直线
,动直线
垂直于
于点
,线段
的垂直平分线交
于点
,设点
的轨迹为
.
(1)求曲线
的方程;
(2)直线
与
交于
两点,求过
两点且与直线
相切的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4180dae966f648d368a10edf3b7e3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b95463a97c60db3250cb641bf6523d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.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/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f334462e4e6c1f68803be0be0d134ac.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4180dae966f648d368a10edf3b7e3c3.png)
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名校
解题方法
9 . 过双曲线
上一点
作两条渐近线的垂线,垂足分别为
,且
.
(1)求双曲线C的标准方程;
(2)若动直线
的斜率存在,且与双曲线
相切,切点为
与双曲线
的两条渐近线分别交于点
,设原点O关于点
的对称点为
,求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a398479977f7106846bb52dbe7ee443.png)
(1)求双曲线C的标准方程;
(2)若动直线
![](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/2533197f8ee31f7b77fb3db1929624ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e406f19e3c1d1f2c85aff4512d8ab90.png)
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解题方法
10 . 已知椭圆
:
的左、右焦点分别是
,
,
是椭圆
上关于原点对称的两点,且
,若
,其中
为坐标原点,则椭圆
的离心率是( )
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27978d1f45f5561b77748870bd3d41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e612d04c57762c74f0b1d0a08599eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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