解题方法
1 . 已知点
,动点
满足
,记点
的轨迹为曲线
.
(1)求
的方程;
(2)若
是
上不同的两点,且直线
的斜率为5,线段
的中点为
,证明:点
在直线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b10869dee07ab7948bfdb81ad58f134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1350897d718a2592dfe8f8ddc5154e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7f8878d628d46bcb847f791857b650.png)
您最近一年使用:0次
2024-03-10更新
|
410次组卷
|
2卷引用:广西百所名校2023-2024学年高二下学期入学联合检测数学试题
2 . 已知椭圆
过点
,焦距为
.过
作直线l与椭圆交于C、D两点,直线
分别与直线
交于E、F.
(1)求椭圆的标准方程;
(2)记直线
的斜率分别为
,证明
是定值;
(3)是否存在实数
,使
恒成立.若存在,请求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ea1f5bdd213c7c3a571b4c38850bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d03fa28c117649b0fdfe17eed7b583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afeda89601db5178bf6f48eb93ef5820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
(1)求椭圆的标准方程;
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afeda89601db5178bf6f48eb93ef5820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0002e26d1bc3291c9c0004ef0cf9c537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7007702bb816d842023ff17e7e8a9d0e.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba14f397c168b2e7fe26b5e38f1bb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-03-06更新
|
481次组卷
|
2卷引用:广西''贵百河“2023-2024学年高二下学期4月新高考月考测试数学试卷
名校
解题方法
3 . 某学校食堂每天中午为师生提供了冰糖雪梨汤和苹果百合汤,其均有止咳润肺的功效.某同学每天中午都会在两种汤中选择一种,已知他第一天选择冰糖雪梨汤的概率为
,若前一天选择冰糖雪梨汤,则后一天继续选择冰糖雪梨汤的概率为
,而前一天选择苹果百合汤,后一天继续选择苹果百合汤的概率为
,如此往复.
(1)求该同学第二天中午选择冰糖雪梨汤的概率.
(2)记该同学第
天中午选择冰糖雪梨汤的概率为
,证明:
为等比数列.
(3)求从第1天到第10天中,该同学中午选择冰糖雪梨汤的概率大于苹果百合汤概率的天数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求该同学第二天中午选择冰糖雪梨汤的概率.
(2)记该同学第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfe0ccc18feef217770312ac21ade7e.png)
(3)求从第1天到第10天中,该同学中午选择冰糖雪梨汤的概率大于苹果百合汤概率的天数.
您最近一年使用:0次
2024-02-27更新
|
1357次组卷
|
5卷引用:广西壮族自治区桂林市2023-2024学年高二下学期入学联合检测卷数学试题
广西壮族自治区桂林市2023-2024学年高二下学期入学联合检测卷数学试题(已下线)专题3.5马尔科夫链模型(强化训练)-2023-2024学年高二数学下学期重难点突破及混淆易错规避(人教A版2019)湖南省三湘创新发展联合体2023-2024学年高三下学期2月开学统试数学试题贵州省黔东南苗族侗族自治州2023-2024学年高三上学期九校联考(开学考)数学试题湖南省邵阳市新邵县第二中学2024届高三下学期开学考试数学试题
4 . 已知圆
经过点
和
,且圆心
在直线
上.
(1)求圆
方程;
(2)若圆
的方程为
,判断圆
与圆
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c59f0e35b7ae5206e45878934482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cab5c6534e43f0ecc54a311a16df80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c6d3c99b7004603ba9ea9c341b8b3f.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e318cefab1d71238b6a770e9d5fe154e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
解题方法
5 . 已知数列
的前
项和为
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a4c566c8868d27f60fa18d9a04b108.png)
(1)求
的通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a4c566c8868d27f60fa18d9a04b108.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e12313d8f1a3fff9dbefd3e3e049f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
23-24高二上·山东德州·期末
名校
解题方法
6 . 已知
,求下列各式的值:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b88b70c1697456f9a8e7f271d6c12e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88391abda888e4fd81a30d364085b3f1.png)
您最近一年使用:0次
2024-02-14更新
|
1080次组卷
|
6卷引用:广西壮族自治区钦州市浦北县浦北中学2023-2024学年高二下学期3月月考数学试题
广西壮族自治区钦州市浦北县浦北中学2023-2024学年高二下学期3月月考数学试题(已下线)山东省德州市2023-2024学年高二上学期期末考试数学试题(已下线)第六章 计数原理(单元测试)-2023-2024学年高二数学同步精品课堂(人教A版2019选择性必修第三册)(已下线)专题2.4二项式定理(八个重难点突破)-2023-2024学年高二数学下学期重难点突破及混淆易错规避(人教A版2019)(已下线)专题01计数原理、排列组合、二项式定理9种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(人教B版2019选择性必修第二册)(已下线)大招7 赋值法
解题方法
7 . 如图,在四棱锥
中,
底面
,底面
是直角梯形,
,
,
点在
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/152e4b02-5d84-43bb-87aa-aa67046eb860.png?resizew=154)
(1)求证,平面
平面
;
(2)若直线
与平面
所成的角为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ff6d7dd48b57f03d82d2c522ee9b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b4dda2be941a16fdfe67ac9aa90298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ab1959f7fa560977ffb9fb0e11bb2c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/152e4b02-5d84-43bb-87aa-aa67046eb860.png?resizew=154)
(1)求证,平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8981acad5791c9037b86779e4d8323.png)
您最近一年使用:0次
解题方法
8 . 如图,在正方体
中,
为平面
的中心.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/1ee695fe-0aca-4c2d-8ef3-c50b6aed425f.png?resizew=159)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa7168302e524813426a0fa494c86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/1ee695fe-0aca-4c2d-8ef3-c50b6aed425f.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d28074ee5af1441242700388b3a9c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
您最近一年使用:0次
9 . 如图,四边形
是一块长方形绿地,
是一条直路,交
于点
,交
于点
,且
.现在该绿地上建一个标志性建筑物,使建筑物的中心到
三个点的距离相等.以点
为坐标原点,直线
分别为
,
轴建立如图所示的直角坐标系.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/c42ec9a0-7c79-46fd-9935-534367339523.png?resizew=140)
(1)求出建筑物的中心
的坐标;
(2)由建筑物的中心到直路
要开通一条路,已知路的造价为150万元
,求开通的这条路的最低造价.
(附:参考数据
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b915251edf729c1e3d86edc68c05cc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554e31ce2d5c31a429a2fceb44156840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c67354b5eaa433b3114be6f559b0d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b337a09a149e222af0d636d3d63edb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/c42ec9a0-7c79-46fd-9935-534367339523.png?resizew=140)
(1)求出建筑物的中心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)由建筑物的中心到直路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cce6cac0fdd4b1a434af8bcaec8fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98024ce2e23a5e81b2bcdd7c96ccef9.png)
(附:参考数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb8e063747281398c27620b4d25bc0c.png)
您最近一年使用:0次
名校
解题方法
10 . 已知过抛物线
的焦点F,斜率为2的直线交抛物线于A,B两点,且
.
(1)求抛物线的方程;
(2)抛物线的准线与x轴交于点
,过点
的直线l交抛物线于M,N两点,当
时,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48867e261c61d24a0a1a4f7ff4627c3.png)
(1)求抛物线的方程;
(2)抛物线的准线与x轴交于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e55590555905eb4f57889bbd16e39a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e55590555905eb4f57889bbd16e39a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdad5be85efb997496d8845f9f70272c.png)
您最近一年使用:0次