解题方法
1 . (1)已知P是直线
上一点,
(
为实数,且
),点
的坐标分别为
,求点P的坐标
.
(2)已知平面上三点A、B、C的坐标分别是
,小明在点B处休憩,有只机器狗沿着
所在直线来回跑动.当机器狗在什么位置时,离小明最近?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b5bb87687b19fbc48be9068db60da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c87f4c40e50504adaface510404dbfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594fa9a4bce1ed5fd27e4cb55d63cf0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8be368791da55817b64a14a89fcf24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
(2)已知平面上三点A、B、C的坐标分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9c2a68bb128cdd92cdd103b0fedc03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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2 . 已知函数
,将
图像上所有点的横坐标伸长到原来的2倍,而纵坐标保持不变,得到函数
的部分图像如图所示,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b2e285758984e8613fa1b52d674c8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6460400186f2b74ece79c861ceb063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
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解题方法
3 . 已知以
为左、右焦点的双曲线
的一条渐近线为
.点
是双曲线
上异于顶点的动点,若
是
的平分线上的一点,且
,则
的取值范围是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0b0da26aac472886b8345cfb9bf8ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8398a001fcf2bc80b13cce4ca1caa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4586226c7e189c5f55f6e9f61c474efb.png)
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4 . 已知平面非零向量
的模均为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799ad95449b4135dee2890ac31c43706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc983f1bad03411ae64d84ff7bdf2551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a16710403d8a87b858d92647ebaa1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
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5 . 已知
,
,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266ad08c70080e52495117cb8307fd3d.png)
(1)求函数
的值域;
(2)求函数
,
的单调减区间;
(3)若
,
恰有2个零点
,求实数
的取值范围和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35005965ce7f4b9703cba4062b6f3053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3328a5bbf1db60229da59fbee7675e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266ad08c70080e52495117cb8307fd3d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b0339e96e32d6fa1a092824850ef8d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43281072ba152ac733bbd50550ffe1a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86251951bb66bd5b40c2fac797f5c074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
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解题方法
6 . “用一个不垂直于圆锥的轴的平面截圆锥,当圆锥的轴与截面所成的角不同时,可以得到不同的截口曲线”,利用这个原理,小强在家里用两个射灯(射出的光锥视为圆锥)在墙上投影出两个相同的椭圆(图1),光锥的一条母线恰好与墙面垂直.图2是一个射灯投影的直观图,圆锥
的轴截面
是等边三角形,椭圆
所在平面为
,则椭圆
的离心率为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745e0525a41fe2e2a7739c75a942290b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4b27f503ce08bc7851006a98f9ce32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
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解题方法
7 . 若任取正方体
的12条棱中的一条棱,则这条棱所在直线平行于平面
的概率为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
8 . 已知函数
是定义在
上的偶函数,当
时,
,当
时,
的表达式为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8180bc243aad2b7736998b10aa2b571a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知关于
的方程
有四个互不相等的根,若这四个根在复平面上对应的点共圆,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d26154aeb0a3a04910123aec2919a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 己知等差数列
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a4222d88c26774f9307e18138eaa32.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ebaff03c5c3eb3a3127f06c784bf58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a4222d88c26774f9307e18138eaa32.png)
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