1 . 已知点
,
,
为坐标原点
(1)若
,
,
无法构成三角形,求
;
(2)若
为直角三角形,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c59f0e35b7ae5206e45878934482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d070a64de8480a0f70a49e447574b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)若
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2 . 如图,已知直角梯形
中,
,过点C作
于点E,M为
的中点.
;
(2)D,M,B三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2590a5a53ebdcd6400cc24d527d4139e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f913298f0fae9f55377a8deab9f099dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a078495ba47076ccaa28b46f765d80.png)
(2)D,M,B三点共线.
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3 . 如图,正方形
的边长为6,E是
的中点,F是
边上靠近点B的三等分点,
与
交于点M.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/cb5deeb6-deaa-447a-9452-0f30e1d6d5e4.png?resizew=134)
(1)求
的值;
(2)已知点P是正方形
四条边上的动点,若
,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/cb5deeb6-deaa-447a-9452-0f30e1d6d5e4.png?resizew=134)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d415c64c7ec3c451f5bcf121c4efde.png)
(2)已知点P是正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b3f53e2e510f7759ba59ff0dbf9728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
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4 . 已知向量
为坐标原点.
(1)当
时,求
与
的夹角的余弦值;
(2)若
三点共线,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41f2f85639241c026d4c8a1723153a0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e368f1b7109436bb94f40363544ffec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e314d99c7a237fd383f155c33e35f73c.png)
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2021-08-26更新
|
304次组卷
|
2卷引用:江苏省南京市鼓楼区2020-2021学年高一下学期期中数学试题
解题方法
5 . 已知抛物线
和
的焦点分别为
和
,且
.
(1)求
的值;
(2)若点
和
是直线
分别与抛物线
和
的交点(异于原点),连接
并延长交抛物线
于
,连接
并延长交抛物线
于
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700ad7aed07a63e122201c04aee41aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e024c990f50078447b1c2f5642844a68.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/a8d6c11ba57b8300a54187717c15c9c1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若点
![](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/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb46dfe874c81668dff7678aa04c5e7.png)
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2021-12-03更新
|
311次组卷
|
3卷引用:江苏省连云港市2021-2022学年高二上学期期中数学试题
6 . 如图,已知椭圆
,
分别为其左、右焦点,过
的直线与此椭圆相交于
两点,且
的周长为8,椭圆
的离心率为
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)在平面直角坐标系
中,已知点
与点
,过
的动直线
(不与
轴平行)与椭圆相交于
两点,点
是点
关于
轴的对称点.求证:
(i)
三点共线.
(ii)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2edae01494aa24d0489e473348b0742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75ebcf0d951f833ca90e040f3cd4db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26453fa6090a097169bf0a8adc9996d.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a97e38fffbca986dee7e2cb28bb794.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/b6268b14-1df5-41d4-b2cb-5c9eefbd3674.png?resizew=197)
您最近一年使用:0次
2019-04-14更新
|
655次组卷
|
3卷引用:【区级联考】北京市门头沟区2019届高三3月综合练习数学试题(理)
名校
7 . 平面直角坐标系xOy内,点
,动点
和Q关于原点O对称,
,
.
(1)以原点O和点A为顶点作等腰直角三角形ABO,使
,求向量
坐标;
(2)若
且P、M、A三点共线,求
的最小值;
(3)若
,且
,
,求直线AQ的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8293156150e4eb50a1bdd71090917dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)以原点O和点A为顶点作等腰直角三角形ABO,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96d9e134e1820d80612be1bc590993e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329fdf7d989f77a32ca9e0361a9cc956.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881a9727fa891bd80ac7c64abb0518ab.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9703534eceb8ccbfebb7a4510d5530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bbff91df26858f512a572c81907716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36753c437b2799a0afa028ae919f8b4c.png)
您最近一年使用:0次
20-21高一·全国·课后作业
解题方法
8 . 已知点A(x,0),B(2x,1),C(2,x),D(6,2x).
(1)求实数x的值,使向量
共线;
(2)当向量
共线时,点A,B,C,D是否在一条直线上?
(1)求实数x的值,使向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39df67384d5bc03635e97e88eb61d0c3.png)
(2)当向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39df67384d5bc03635e97e88eb61d0c3.png)
您最近一年使用:0次
名校
解题方法
9 . 在平面直角坐标系中,已知点
,
,
.
(1)若
三点共线,求实数
的值;
(2)若直线
与直线
垂直,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb0d9465a2306dfa02d5498cdf1bf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d3bfa155ad67018da4d65815c5e5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11dd167e5b6eb85fdc5dc62ed32c8075.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2021-10-29更新
|
276次组卷
|
9卷引用:陕西省黄陵中学2018届高三(重点班)上学期期中考试数学(理)试题
陕西省黄陵中学2018届高三(重点班)上学期期中考试数学(理)试题山东省菏泽市第一中学2017-2018学年度高一第一学期第二次月考数学试题安徽省亳州市第一中学2021-2022学年高二上学期9月教学检测数学试题河北省石家庄市二十七中2021-2022学年高二上学期第一次月考(10月)数学试题天津市实验中学滨海学校2021-2022学年高二上学期10月月考数学试题(已下线)专题37 两直线位置关系-学会解题之高三数学万能解题模板【2022版】沪教版(2020) 选修第一册 领航者 期中测试黑龙江省大庆市让胡路区大庆中学2022-2023学年高一下学期期中数学试题河北省邯郸市鸡泽县第一中学2023-2024学年高二上学期第一次月考数学试题
10 . (1)已知向量
,
,
,求
的值.
(2)已知
,
,
与
共线且方向相同,求x.
(3)设向量
,
,
,求当k为何值时,A,B,C三点共线?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4984318d967b210ce49f126794dad06b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ab5f93cd89ae2800ce9be4010c1942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b6df25cc264ccbd6751744b639227b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbed0be31807c33c5211552795ba364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98fda9dda9563cdf560084043c5c1abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
(3)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c41da2daaa43bae07f19bc20163170c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fde405d3fc28302fcac65b8c1d1b249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9213c690379b159493d8843959d5131.png)
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