1 . 已知平面直角坐标系中的点
的坐标x,y满足
,记
的最大值为M,最小值为m.
(1)请说明P的轨迹是怎样的图形;
(2)求
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9db1fea04fda2b8aec3893816bb990a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7a5220a93b56c59c5934d144784a59.png)
(1)请说明P的轨迹是怎样的图形;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed83485b04357536c07c06cdd74f149.png)
您最近一年使用:0次
2020-04-13更新
|
217次组卷
|
6卷引用:陕西省渭南市韩城市2019-2020学年高二上学期竞赛考试数学试题
陕西省渭南市韩城市2019-2020学年高二上学期竞赛考试数学试题(已下线)专题09 直线与圆、圆与圆的位置关系-2020-2021学年高中数学新教材人教A版选择性必修配套提升训练沪教版(2020) 选修第一册 单元训练 第2章 单元测试(已下线)第2章 圆锥曲线【单元提升卷】-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)2.4.2 圆的一般方程【第三课】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)2.4.2 圆的一般方程【第二课】“上好三节课,做好三套题“高中数学素养晋级之路
解题方法
2 .
、
是已知圆
的两条互相垂直的半径,延长
至点P,延长
至点Q.使得
,
.
(1)若直线OP和OQ的斜率都存在,试确定直线OP和OQ的斜率的乘积是否为一个常数?
(2)试确定
是否为一个常数?
(3)设
.试确定是否存在两个定点
、
,使
,
的斜率的乘积为一个常数?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88ec2dbad3fa6208c0493291e5ccdcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f304a24bb2e199772c53223db7b4be9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88ec2dbad3fa6208c0493291e5ccdcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f304a24bb2e199772c53223db7b4be9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d388a3e54d3a0a19d064fc7ca00459b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799a839722766253265f9da8d582982b.png)
(1)若直线OP和OQ的斜率都存在,试确定直线OP和OQ的斜率的乘积是否为一个常数?
(2)试确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc54eca5a663aa7a6bc2273bc05869d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074185b639a471cbc8107e54bac0fe66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c2cc110e46ae4b3432814810e28bcf.png)
您最近一年使用:0次
名校
3 . 在平面直角坐标系xOy中,圆O:x2+y2=4与x轴的正半轴交于A,以A为圆心的圆A:(x﹣2)2+y2=r2(r>0)与圆O交于B,C两点.
![](https://img.xkw.com/dksih/QBM/2021/4/5/2693511761510400/2693817838600192/STEM/be149aba-5fe2-4a59-ab1b-a478d7fe2880.png)
(1)求
的最小值;
(2)设P是圆O上异于B,C的任一点,直线PB,PC与x轴分别交于点M,N,求S△POM•S△PON的最大值.
![](https://img.xkw.com/dksih/QBM/2021/4/5/2693511761510400/2693817838600192/STEM/be149aba-5fe2-4a59-ab1b-a478d7fe2880.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b89e7ff008dea7530bdc4ea5b6419d.png)
(2)设P是圆O上异于B,C的任一点,直线PB,PC与x轴分别交于点M,N,求S△POM•S△PON的最大值.
您最近一年使用:0次
2021-04-06更新
|
535次组卷
|
7卷引用:2015年全国高中数学联赛陕西赛区预赛试题
2015年全国高中数学联赛陕西赛区预赛试题(已下线)【新东方】杭州新东方高中数学试卷351浙江省杭州市学军中学(西溪校区)2020-2021学年高二上学期期中数学试题(已下线)黄金卷17-【赢在高考·黄金20卷】备战2021年高考数学全真模拟卷(江苏专用)(已下线)专题10 《直线和圆的方程》综合测试卷 - 2021--2022高二上学期数学新教材配套提升训练(人教A版2019选择性必修第一册)(已下线)专练29 期中综合检测卷(A卷)-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)江苏省南通市如东县2022-2023学年高二上学期10月阶段测试数学试题
4 . 若以
为一个顶点,试在
轴上找一点B,另在直线
上找一点C,使构成的
的周长最小,并求出此时
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17ff5e0a917684d41cd41e0ae303308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb31826e94cde6199ed7f93139f3e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2019-10-11更新
|
55次组卷
|
2卷引用:第一届高二试题(初赛)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
5 . 已知两个边长为
的正三角形
与
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/6a89a8f1-c5cd-4406-9093-0b1107198640.png?resizew=154)
(
)当
的距离为多少时,三棱锥
的体积最大?
(
)求三棱锥
的体积最大时的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/6a89a8f1-c5cd-4406-9093-0b1107198640.png?resizew=154)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
解题方法
6 . 如图
,直角梯形
,
,将
沿
折起来,使平面
平面
.如图
,设
为
的中点,
,
的中点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/5724be25-5478-45c0-87f3-a77dc61d8262.png?resizew=418)
(
)求证:
平面
.
(
)求平面
与平面
所成锐二面角的余弦值.
(
)在线段
上是否存在点
,使得
平面
,若存在确定点
的位置,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a717c411ecb25464d817d7c2e807164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4cb0b82547733eef4343354bb7c791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/5724be25-5478-45c0-87f3-a77dc61d8262.png?resizew=418)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df82499e4eaac32e09290faf3d2a166b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd0b0bda79a950fe6f44fc6d62740f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
7 . 如图,在四棱锥P−ABCD中,底面ABCD是菱形,∠DAB=60°,PD⊥平面ABCD,PD=AD=1,点E,F分别为AB和PD中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/e62f477e-0eff-410d-ab5f-9aaf90e4a44b.png?resizew=170)
(1)求直线AF与EC所成角的正弦值;
(2)求PE与平面PDB所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/e62f477e-0eff-410d-ab5f-9aaf90e4a44b.png?resizew=170)
(1)求直线AF与EC所成角的正弦值;
(2)求PE与平面PDB所成角的正弦值.
您最近一年使用:0次
名校
8 . 如图,多面体ABCDE中,四边形ABED是直角梯形,∠BAD=90°,DE∥AB,△ACD是的正三角形,CD=AB=
DE=1,BC=![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/d89e000f-a5b7-41ba-9631-e0638fd483ee.png?resizew=170)
(1)求证:△CDE是直角三角形
(2) F是CE的中点,证明:BF⊥平面CDE
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/d89e000f-a5b7-41ba-9631-e0638fd483ee.png?resizew=170)
(1)求证:△CDE是直角三角形
(2) F是CE的中点,证明:BF⊥平面CDE
您最近一年使用:0次
2019-01-02更新
|
234次组卷
|
2卷引用:【全国百强校】湖南省衡阳市第一中学2018-2019学年高一上学期六科联赛数学试题
9 . 在四面体ABCD中,过棱AB的上一点E作平行于AD,BC的平面分别交四面体的棱BD,DC,CA于点F,G,H
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/0eac358e-d7aa-4e75-b4fd-cbe363f87349.png?resizew=152)
(1)求证:截面EFGH为平行四边形
(2)若P、Q在线段BD、AC上,
,且P、F不重合,证明:PQ∥截面EFGH
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/0eac358e-d7aa-4e75-b4fd-cbe363f87349.png?resizew=152)
(1)求证:截面EFGH为平行四边形
(2)若P、Q在线段BD、AC上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7071b5ecb076a09f8d128c58f01220ee.png)
您最近一年使用:0次
10 . 如图,设
为正方形
所在平面外一点,点
分别在
上,且
.证明:直线
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60ed701b319dbdf1541a17e8da003f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/784bf07e745ca00fc0f8e8f4c0343b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ce5b706ae738b30640c0d44174a739.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/a68b3c38-9043-4a12-82e1-053c850503e1.png?resizew=144)
您最近一年使用:0次
2018-12-28更新
|
199次组卷
|
6卷引用:数学奥林匹克高中训练题(150)