解题方法
1 . 已知双曲线
,则双曲线( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
A.焦点坐标为![]() ![]() |
B.渐近线方程为![]() ![]() |
C.离心率为![]() |
D.与直线![]() |
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2 . 如图,三棱柱
中,侧棱
底面ABC,且各棱长均相等,D,E,F分别为棱AB,BC,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/48d2aca1-6308-4fa7-8c42-2d9e01b65657.png?resizew=180)
(1)证明
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/48d2aca1-6308-4fa7-8c42-2d9e01b65657.png?resizew=180)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
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3 . 已知椭圆
的左右焦点分别
,若______.
请把以下两个条件中任选一个补充在横线上作答(若都选择,则按照第一个解答给分)
①四点
中,恰有三点在椭圆C上.
②椭圆C经过
,
轴,且
.
(1)求椭圆C的方程;
(2)设点D为椭圆C的上顶点,过点D作两条互相垂直的直线分别交椭圆于A、B两点,过D作直线AB的垂线垂足为M,判断y轴上是否存在定点N,使得
为定值?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
请把以下两个条件中任选一个补充在横线上作答(若都选择,则按照第一个解答给分)
①四点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedfac2568f82d62e1afd663ca6efcd7.png)
②椭圆C经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827d2dba1eefc6237b6808e058d45f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47fb32b931ef1125d7a241d1c829e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f27b6070d21b6a3fb46e522b8b8bb2.png)
(1)求椭圆C的方程;
(2)设点D为椭圆C的上顶点,过点D作两条互相垂直的直线分别交椭圆于A、B两点,过D作直线AB的垂线垂足为M,判断y轴上是否存在定点N,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4ea7acf140086ae816a4025d2683dc.png)
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解题方法
4 . 设圆C的圆心在直线
上,圆C与直线
相切于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ebd2da016e7029c4dd72b9e377190c.png)
(1)求圆C的方程;
(2)过点
的直线与圆C相交于A、B.若
,求直线AB的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4407788e4dc88210bca71a2551d4f2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ebd2da016e7029c4dd72b9e377190c.png)
(1)求圆C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ebd2da016e7029c4dd72b9e377190c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
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解题方法
5 . 如图,一种电影放映灯的反射镜面是旋转椭圆面(椭圆绕其对称轴旋转一周形成的曲面)的一部分,过对称轴的截口
是椭圆的一部分,灯丝位于椭圆的一个焦点
上,片门位于另一个焦点
上,由椭圆一个焦点
发出的光线,经过旋转椭圆面反射后集中到另一个焦点
.已知
,
,
,则光从焦点
出发经镜面反射后到达焦点
经过的路径长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb49d869110f27140f5c1934143db2e.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed32c58a5f0141375ce87cc5a2e5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486dd1cfbf14bb8a88be8061b4d86087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b6b25851f84257fd6b97d00f69a99d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/4c17c10d-299e-474b-89a0-daf3f8741dc3.png?resizew=176)
A.5 | B.10 | C.6 | D.9 |
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解题方法
6 . 在正方体
中,
是
的中点,则异面直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 如图,在边长为2的正方形
中,点
是
的中点,点
是
的中点,将
分别沿
折起,使
三点重合于点
,则下列判断正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/0a3d3f86-8b65-4e45-a0f8-317800c48457.png?resizew=150)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b697b4ff810b1aa81570528832e94c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aade83af002b001a9367c2226dcfcda0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/0a3d3f86-8b65-4e45-a0f8-317800c48457.png?resizew=150)
A.![]() |
B.平面![]() ![]() |
C.三棱锥![]() ![]() |
D.三棱锥![]() ![]() |
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8 . 如图,圆柱形容器内部盛有高度为8cm的水,若放入三个相同的球(球的半径为圆柱的底面半径相同)后,水恰好淹没最上面的球(如图所示),则每个球的表面积为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ce13774b09ff2edddaf21a072cf60a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/b879e724-355a-418f-85b3-7816dd828b95.png?resizew=78)
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解题方法
9 . 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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10 . 已知直线
的方程为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e6441a7e417f74ed0747543b9d66c7.png)
A.倾斜角为![]() | B.倾斜角为![]() |
C.方向向量可以为![]() | D.方向向量可以为![]() |
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