名校
解题方法
1 . 已知函数
(其中
在
上单调递减,点
,
,
是函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
图象上三点,满足
.
(1)求证:
,
,
三点不共线;
(2)求证:
是钝角三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8acdbf533b367bbd207e267e7e4d22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d9cd8123d0c0a8cf2d8007abb79397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dddee525114c09ee0d1205aed6e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3b54e0dcdc081d45fb3df933cddc29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f73eaf35877e7cb4eff9ce6c81655c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97fc87d1c6bec952eb132bf884b15fbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9440f2d7ae0b2039fd68e50aec92d55f.png)
(1)求证:
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
解题方法
2 . 在直角坐标系
中,设
为抛物线
的焦点,
为
上位于第一象限内一点.当
时,
的面积为1.
(1)求
的方程;
(2)当
时,如果直线
与抛物线
交于
两点,直线
的斜率满足
. 证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a5f7aa32000ae7ed868721278834bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2ce6d23fb52cc513580a8f0e6760c2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e30c5909e71d420de79eadd5061cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03df57efff473b3cfeb8503796b7d6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2c1be4b46eb936b47e4ca870922fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
3 . (1)证明:当
时,
;
(2)若过点
且斜率为
的直线
与曲线
交于
两点,
为坐标原点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468ddff079eafd5b6062e230f8ed42a.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803dc3c76fd2b51696647aa18602412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0482468ee9123843cc9310b1fd7a27b4.png)
您最近一年使用:0次
4 . 在直角坐标系
中,以
为始边分别作角
,
,其终边分别与单位圆交于点
,
.
(1)证明:
;
(2)已知
,
为锐角,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e4c210b2342523b23a43e0a5fd4f63.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e82e61189eee22b8a316b16ead9fed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccd1dfdc167165bcad456709247c723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800db22e042a298041eda8b0c72abb7c.png)
您最近一年使用:0次
2023-04-04更新
|
172次组卷
|
2卷引用:贵州省贵阳市三新改革联盟校2022-2023学年高一下学期4月联考数学试题
名校
5 . 如图,已知
为平行四边形.
,
,
,求
及
的值;
(2)记平行四边形
的面积为
,设
,
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8ffec55dc1c43b460a8fef3a468d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7872abd162e356132bb371fc581d818c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b0246acc9bed97eef80edc52bcb37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bad16b7cdf8c638cd324f5be5d834f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a10f2c4a2a9c9cb4047f9f27cff1d7a.png)
(2)记平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1018d072c74bd0f5f013002751e16668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f021b99eb4724a997686d8ab1585382b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187d580a038d49b541c40a7e56b60c17.png)
您最近一年使用:0次
2023-07-08更新
|
544次组卷
|
4卷引用:上海市黄浦区2022-2023学年高一下学期期末数学试题
上海市黄浦区2022-2023学年高一下学期期末数学试题江苏省无锡市辅仁高级中学2023-2024学年高一下学期3月月考数学试卷(已下线)专题02 平面向量-《期末真题分类汇编》(上海专用)(已下线)专题05向量数量积期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)
6 . 已知向量
、向量
、向量
,其中
.
(1)求证:
;
(2)设函数
,求
的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4352ee613a54dfb490a8f5f15168215f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f24da204ce64046ce68248c8a82d9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f343b247707352ff51723fb9aef16a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc712ef9309d018fa58b86de657d6a45.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f694e42b337503dfb7466a3da23ab4.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea46fd6339d369a098adc6d8206d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,已知动圆
过定点
且与
轴相切,点
关于圆心
的对称点为
,点
的轨迹为
.
(1)求曲线
的方程;
(2)一条直线
经过点
,且交曲线
于
、
两点,点
为直线
上的动点.
①求证:
不可能是钝角;
②是否存在这样的点
,使得
是正三角形?若存在,求点
的坐标;否则,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/9309316d-b548-4c36-beaf-7d0f2b60fc33.png?resizew=145)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)一条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1c84057882768f20a01365c81b6760.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
②是否存在这样的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2023-09-19更新
|
645次组卷
|
9卷引用:江西省南昌市第二中学2019-2020学年高二上学期期中数学(理)试题
江西省南昌市第二中学2019-2020学年高二上学期期中数学(理)试题(已下线)第2章 圆锥曲线(基础、常考、易错、压轴)分类专项训练(1)(已下线)高二下期中真题精选(常考60题专练)-【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)高二上学期期中【常考60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)福建省厦门双十中学漳州校区2024届高三上学期10月月考数学试题(已下线)专题突破卷23 圆锥曲线大题归类(已下线)考点19 解析几何中的探索性问题 2024届高考数学考点总动员【练】湖北省武汉市武昌实验中学2023-2024学年高二上学期12月月考数学试题(已下线)模块五 专题6 期末全真模拟(拔高卷2)期末终极研习室(高二人教A版)
名校
解题方法
8 . 已知椭圆
,
是椭圆上的两个不同的点,
为坐标原点,
三点不共线,记
的面积为
.
(1)若
,求证:
;
(2)记直线
的斜率为
,当
时,试探究
是否为定值并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117de32547b9d58f3d102ec4c9b3bfc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aa828f2bd9a5e63ee58dcaa9d0d336.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/21/ba783b5d-4619-4335-aad4-d58e1e2a617c.png?resizew=213)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7332a5f0775000d42536c39a414fb66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7e00545464c5bb080ab5ddf22bf491.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eac9ba606fb477550aa62db7bfa0ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5263f41aa7aa7a5ecbaed1a0a19c4f5d.png)
您最近一年使用:0次
解题方法
9 . 已知向量
,
,其中
.
(1)若
,写出
,
,
,
之间应满足的关系式
(2)求证:
;
(3)求代数式
的最大值,并求其取得最大值时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300b10194024b776bc5985a76c4021a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b39fbfa2a3a5e3715e3a5855334e143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b398c3c2ffc0b9a08211fcacc87fa7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f709a55cf756727bc6811bc239718281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c184edd63472d8ddf96e5f815515d929.png)
(3)求代数式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048e10bf2ade5fd58144d6b952cdd717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2023高三·全国·专题练习
解题方法
10 . 已知椭圆
过
和
两点.
(1)求椭圆C的方程;
(2)如图所示,记椭圆的左、右顶点分别为A,B,当动点M在定直线
上运动时,直线
,
分别交椭圆于两点P和Q(不同于B,A).证明:点B在以
为直径的圆内.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de261e9b4defbc0be6440397031a87b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8690460339dc7085bf6474942e86d28c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/3/f43924da-53da-4551-bc15-3666fc09d0db.png?resizew=190)
(1)求椭圆C的方程;
(2)如图所示,记椭圆的左、右顶点分别为A,B,当动点M在定直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次