名校
解题方法
1 . 已知O为直线
外一点,
(1)若
,求证:A、B、C三点共线;
(2)若O为坐标原点,
,判断
的形状,并给予证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6aff1c674bff5478b85a2d207f61859.png)
(2)若O为坐标原点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3655a675811b46976a3020c5d11545cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
名校
2 . 张同学在函数章节学习中遇到过许多形形色色的函数,其中有很多函数的形态是具有共性的,于是张同学提出了下面2个猜想,请同学们选择下面的任意一个问题回答或反驳张同学的猜想.
(1)已知函数
的零点是
的零点是
,证明:
.
(2)已知函数
的零点是
,证明:
.
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb113c900e07d80fdcd8afed691b54b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfe04161d6ebd5964979d54faef5c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f700e9e84ec901bf75313a29757740fa.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a1cb7e36c08e6f1822258f65f2865e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6829485c1d817b5eed2e1a81ed0b642d.png)
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3 . 某建筑物的上层框图如图所示,其上下底面是平行的两正方形,上下底面的中心连线垂直于上下地面,且各侧棱均相等(即为正棱台),经测量得知
,侧棱长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/7b28e486-08db-4c9b-b922-fcffe281bd16.png?resizew=265)
(1)求证
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1060dbf8c1a85848754e0717799793.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcf43ba416adeb723cebe4aee6bbe34.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/7b28e486-08db-4c9b-b922-fcffe281bd16.png?resizew=265)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1de5964353beb55c5058b2a431eecaf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6ab5a1695a47751d93ec248ee61eaa.png)
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名校
解题方法
4 . 如图所示,已知椭圆
,过右焦点作两条互相垂直且均不平行于坐标轴的弦
,它们的中点分别为
,延长
分别与椭圆交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/1379cd26-71e3-4654-8adf-54330ec5df63.png?resizew=169)
(1)证明:
斜率之积为定值;
(2)若
,求直线
斜率之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f65dbed884e2248ec075655c684aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/1379cd26-71e3-4654-8adf-54330ec5df63.png?resizew=169)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f65dbed884e2248ec075655c684aa7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad52c964ea3acc0518913e9edcc177c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
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2021-10-17更新
|
432次组卷
|
3卷引用:云南省峨山彝族自治县第一中学2022届高三10月测试数学(文)试题
云南省峨山彝族自治县第一中学2022届高三10月测试数学(文)试题中学生标准学术能力诊断性测试2021-2022学年高三上学期10月测试文科数学试题(已下线)第五篇 向量与几何 专题11 圆锥曲线中的蝴蝶定理 微点3 圆锥曲线中的蝴蝶定理综合训练
解题方法
5 . 直线
交
轴于点
,交椭圆上
(
)于相异两点
,
,且
.
(1)求
的取值范围;
(2)将弦
绕点
旋转
得到线段
,设点
的坐标为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.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/664dd75ac186f08df210f40d98355711.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)将弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e7a123c9cc0e058db28841fb0edcf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffef5fb614a2b2a033451b523a21ac3.png)
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名校
解题方法
6 . 已知双曲线的方程为
,椭圆
的方程为
,双曲线右焦点到双曲线渐近线的距离为
,椭圆的焦点为
,
,短轴端点为
,
.
(1)求双曲线的方程与椭圆的方程;
(2)过点
作椭圆
的两条互相垂直的弦
,
,证明:过两弦
,
中点的直线恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb74c0c2d1e5305cf55cfb9605929268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74404619ad5699e6c44c947fb569600f.png)
(1)求双曲线的方程与椭圆的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed179a90c1a61e30924c515c7d643618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
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7 . 向量是解决数学问题的一种重要工具,我们可以应用向量的数量积来解决不等式等问题.
(1)(ⅰ)若
,
,比较
与
的大小;
(ⅱ)若
,
,比较
与
的大小;
(2)
,
为非零向量,
,
,证明:
;
(3)设
为正数,
,
,
,求
的值.
(1)(ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecf76d71aed3b37bd48550bf48c1086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f683269ae8936d010ba111e9c9be5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a8f20036b1e7cfb0800f141d843718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f01e75d42bcb00df9c20734d9f3c547.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecf76d71aed3b37bd48550bf48c1086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012b990e9c0d9f8da823df2ef36b26dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a8f20036b1e7cfb0800f141d843718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f01e75d42bcb00df9c20734d9f3c547.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee437e6ff470c2f67b8429f57b90ae37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0118005d052d96ec2490facb71145b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04e531f59cead9c6f1017dbf1c953f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79e891ae2a63b7c20e00cb05e9acb71.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93b98eef83e6b1b364a4cd6c55148ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e37739c262e686df999f5b89595c264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc786b1cdc9c0bf814f43abdb1d2ad67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5b9c5de247a0aef2e56f58a88a8698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f4495f96d35d8cb294a872223b923a.png)
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解题方法
8 . 如图,将等腰直角
沿斜边
旋转,使得
到达
的位置,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/b700e49f-33b5-46cf-8904-120b3bf6d21b.png?resizew=157)
(1)证明:平面
平面
.
(2)求二面角
的余弦值.
(3)若在棱
上存在点
,使得
,
,在棱
上存在点
,使得
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90f9fba63790e1e5308fa5a1441d71a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/b700e49f-33b5-46cf-8904-120b3bf6d21b.png?resizew=157)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae50ff4c814b581a78346e548964aae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00f1eaa084baa5272450c34ab1ffde54.png)
(3)若在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffb952f86442845da723fd291564484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1a61e889d0b83ed95a38f1adf4e8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077ad2164c272a0ca4c52f3159b0e486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5987b311288bb1f71556dfe81d936c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79498e1df1280868532f59ee8059a223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
9 . 已知抛物线
的焦点为F,准线与x轴交点为T,点G在E上且
轴,
的面积为
.
(1)求E的方程;
(2)已知点
,
,
,点A是E上任意一点(异于顶点),连接
并延长交E于另一点B,连接
并延长交E于另一点C,连接
并延长交E于另一点D,当直线
的斜率存在时,证明:直线
与
的斜率之比为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4c5119c63ea86e97ad2ac7c84a423b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8afbdf92080953b4093dc30e37aded91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
(1)求E的方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8293156150e4eb50a1bdd71090917dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6129110e508ca0fa4aec666d2684ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33e1e069c283602b5a7844d25b81e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb6fd2fa53b92a03d21f208b74e3857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2021-05-13更新
|
495次组卷
|
3卷引用:云南省昆明市2021届高三三模数学(文)试题
云南省昆明市2021届高三三模数学(文)试题(已下线)第3讲 圆锥曲线中的证明、定值、定点问题(练)-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)宁夏石嘴山市平罗中学2022届高三第四次模拟考试数学(理)试题
名校
解题方法
10 . 将所有平面向量组成的集合记作
,并定义“向量函数”:
,其中
,
.已知
,设
,
,定义向量函数
.
(1)证明:对于任意
,
以及
,
,
恒成立;
(2)若
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5938410a3d39a1f3f4df67faf99ab5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552355ddba8eef1ca3bf15eb53d79622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee410c26fe0a98bc7994b65166191e12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91b0e5ad368c6da34f2263de056fee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f687593cb4ecef31667bf2320fdfe000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88fa4b2313ad1f74634fb9e6cdd7627e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa48cf7be8957cd677297267735bee62.png)
(1)证明:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e28e412a5710cf13b3cf2159056089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5a523e020e21797c0f83c2b6772588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e87f257ae0356956f4ca8dc3deb189.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e28e412a5710cf13b3cf2159056089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedbff5fec9d9d0bdbbcf6e87f7f0876.png)
您最近一年使用:0次