名校
1 . 如图,在正三棱柱
中,
,
为
的中点,
、
在
上,
.
(1)试在直线
上确定点
,使得对于
上任一点
,恒有
平面
;(用文字描述点
位置的确定过程,并在图形上体现,但不要求写出证明过程)
(2)已知
在直线
上,满足对于
上任一点
,恒有
平面
,
为(1)中确定的点,试求当
的面积最大时,二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa40b456747f69437444833aab387be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2564f406fa222935e6d5bb24df0356a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/c34c1d0d-b0de-4ab5-8ff6-a1140bfc6c2c.png?resizew=127)
(1)试在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de8026bd1b6af298df08e532c2847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826bf6fa3706921b77ad0eb4fcc206bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de8026bd1b6af298df08e532c2847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b17d7abbd564ce785f43a7c8526dc03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ef68c72248af27e3b83b4ee5fdeb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6b513ee7d966df71cd98b29ca4447e.png)
您最近一年使用:0次
2023-07-09更新
|
860次组卷
|
6卷引用:福建省厦门市第一中学2023-2024学年高二上学期开学考试数学试题
福建省厦门市第一中学2023-2024学年高二上学期开学考试数学试题福建省泉州市2022-2023学年高一下学期期末教学质量监测数学试题福建省永春第一中学2023-2024学年高一上学期8月月考数学试题(已下线)10.4 平面与平面间的位置关系(第2课时)(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)专题04 立体几何初步(2)-【常考压轴题】(已下线)第二章 立体几何中的计算 专题一 空间角 微点10 二面角大小的计算综合训练【培优版】
名校
2 . 如图,某日的钱塘江观测信息如下:2017年
月
日,天气:阴;能见度:1.8千米;
时,甲地“交叉潮”形成,潮水匀速奔向乙地;
时,潮头到达乙地,形成“一线潮”,开始均匀加速,继续向西;
时,潮头到达丙地,遇到堤坝阻挡后回头,形成“回头潮”.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/1e0cd8ba-dbdb-44f6-a0e7-e9515f7bc398.png?resizew=547)
按上述信息,小红将“交叉潮”形成后潮头与乙地质检的距离
(千米)与时间
(分钟)的函数关系用图3表示.其中:“
时甲地‘交叉潮’的潮头离乙地12千米”记为点
,点
坐标为
,曲线
可用二次函数:
,
是常数)刻画.
(1)求
值,并求出潮头从甲地到乙地的速度;
(2)
时,小红骑单车从乙地出发,沿江边公路以0.48千米
分的速度往甲地方向去看潮,问她几分钟与潮头相遇?
(3)相遇后,小红立即调转车头,沿江边公路按潮头速度与潮头并行,但潮头过乙地后均匀加速,而单车最高速度为0.48千米
分,小红逐渐落后.问小红与潮头相遇到落后潮头1.8千米共需多长时间?(潮水加速阶段速度
,
是加速前的速度)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ded97417d5d9595c6ef28a8870b5252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7719df082f37fffa9696c95fb35dfd17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4debe81a50c2d32980990f8dc343033.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/1e0cd8ba-dbdb-44f6-a0e7-e9515f7bc398.png?resizew=547)
按上述信息,小红将“交叉潮”形成后潮头与乙地质检的距离
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ded97417d5d9595c6ef28a8870b5252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c01b56efbe3bc21c47daa1c2a8b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67c623950b5795d5fb4daeb8102a8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f0eca99faee0cf36337f6996b5cd81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0c6f8da459cd3797ef774c4e34c436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4333bb203d02814c146ed587b69ea69d.png)
(3)相遇后,小红立即调转车头,沿江边公路按潮头速度与潮头并行,但潮头过乙地后均匀加速,而单车最高速度为0.48千米
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4333bb203d02814c146ed587b69ea69d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce1a4b20f47e160b88b557ca8a8fe76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f58888df91890a19a1aa7511d19703f.png)
您最近一年使用:0次
名校
3 . 边长为
的正方形
中,
是对角线
上的一个动点(点
与A、
不重合),连接
,将
绕点
顺时针旋转
到
,连接
,
与
交于点
,
延长线与
(或
延长线)交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/4c80a369-f2ac-45d4-98d0-699c97c32465.png?resizew=188)
(1)连接
,证明:
;
(2)设
,
,试写出
关于
的函数关系式,并求当
为何值时,
;
(3)猜想
与
的数量关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f6927cc2a930203ac34366383e76ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f6927cc2a930203ac34366383e76ef.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/56f6927cc2a930203ac34366383e76ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/4c80a369-f2ac-45d4-98d0-699c97c32465.png?resizew=188)
(1)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1294b21ef6800dfdabe426d34e8b563.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8711eddf26d11fc974dfb6da4b640918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e21bf3bb41f4648070c41f0f283945c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d33329e0e6712174ea9e301ee0be506.png)
(3)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15febfda66e733f14aa7115ed4343a8.png)
您最近一年使用:0次
名校
解题方法
4 . 端午节当天,小明带了四个粽子(除味道不同外,其它均相同),其中两个是大枣味的,另外两个是火腿味的,准备按数量平均分给小红和小刚两个好朋友.
(1)请你用树状图或列表的方法表示小红拿到的两个粽子的所有可能性.
(2)请你计算小红拿到的两个粽子刚好是同一味道的概率.
(1)请你用树状图或列表的方法表示小红拿到的两个粽子的所有可能性.
(2)请你计算小红拿到的两个粽子刚好是同一味道的概率.
您最近一年使用:0次
名校
5 . 滴滴快车是一种便捷的出行工具,计价规则如表:
小王与小张各自乘坐滴滴快车,行车里程分别为6公里与8.5公里.如果下车时两人所付车费相同,那么这两辆滴滴快车的行车时间相差___________ .
计费项目 | 里程费 | 时长费 | 远途费 |
单价 | 1.8元![]() | 0.3元![]() | 0.8元![]() |
注:车费由里程费、时长费、远途费三部分构成,其中里程费按行车的实际里程计算;时长费按行车的实际时间计算;远途费的收取方式为:行车里程7公里以内(含7公里)不收远途费,超过7公里的,超出部分每公里收0.8元. |
您最近一年使用:0次
6 . 如图,
是矩形
内的任意一点,连接
、
、
、
,得到
、
、
、
,设它们的面积分别是
,
,
,
,给出如下结论:①
;②
;③若
,则
;④若
,则
点在矩形的对角线上.其中正确的结论的个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/d2388f26-6135-4875-a8cb-8bd75b882187.png?resizew=206)
![](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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8fe4026f1a0745ab9aa9fe64f0e482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a53c1ed888b57b17c2c44207a439ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315bb82e2dfa00423ca48635305e8203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad351432bd46e0fbeabf368e0ab55d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10195d68eb62e0fc5f7d6d0c83da44dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dd78e9156dcf6db93f6cbcc5b43b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/d2388f26-6135-4875-a8cb-8bd75b882187.png?resizew=206)
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
名校
7 . 一只盒子中有
个红球,9个白球,
个黑球,每个球除颜色外都有相同.已知至少摸出17个球时其中一定有5个红球,至少摸出17个球时其中一定有8个相同颜色的球,则代数式
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9077dbb0fe53cedae402a82287060d76.png)
A.7 | B.6 | C.5 | D.4 |
您最近一年使用:0次
名校
8 . 如图1,抛物线
的顶点
在
轴正半轴上,交
轴于点
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/dc0cee2f-1993-4a28-967e-03dc81d4bc36.png?resizew=355)
(1)求抛物线的解析式;
(2)如图2,
是第一象限内抛物线上对称轴右侧一点,过
的直线
与抛物线有且只有一个公共点,
交抛物线对称轴于
点,连
交对称轴于
点,若
,求直线
的解析式;
(3)若点
、
是抛物线的两点,以线段
为直径的圆经过点
,求证:
始终经过一个定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14068b9b324f406b8daf9d4b84adc961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e47e0490783777567ce9ba80a37a20.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/dc0cee2f-1993-4a28-967e-03dc81d4bc36.png?resizew=355)
(1)求抛物线的解析式;
(2)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9de22c289d5e3b5101a720a41155fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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9 . 阅读以下材料,并按要求完成相应的任务:莱昂哈德
欧拉
是瑞士数学家,在数学上经常见到以他的名字命名的重要常数,公式和定理,下面就是欧拉发现的一个定理:在
中,
和
分别为外接圆和内切圆的半径,
和
分别为其中外心和内心,则
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/b1a259a9-1a05-48e4-9259-1977e6f19620.png?resizew=136)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/e5af681c-00bc-49de-b2ce-e7f738fdc6c6.png?resizew=379)
如图1,
和
分别是
的外接圆和内切圆,
与
相切分于点
,设
的半径为
,
的半径为
,外心
(三角形三边垂直平分线的交点)与内心
(三角形三条角平分线的交点)之间的距离
,则有
.
下面是该定理的证明过程(部分)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa96c86a9085aeb7a57ce955200f0c80.png)
延长
交
于点
,过点
作
的直径
,连接
,
.
,
(同弧所对的圆周角相等).
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
,
,①
如图2,在图1(隐去
,
的基础上作
的直径
,
如图2,动手连接
,
,
,
.
是
的直径,所以
.
与
相切于点
,所以
,
.
(同弧所对的圆周角相等),
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
.
②
(1)观察发现:
___________,
___________(用含
,
的代数式表示);
(2)请观察式子①和式子②,并利用任务(1)的结论,按照上面的证明思路,完成该定理证明的剩余部分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97ec04a1aa7ac6fce72d589864940a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942ed7a1f801116d70437254128e17c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95742051f1ab28e701eb18977b9cac3f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/b1a259a9-1a05-48e4-9259-1977e6f19620.png?resizew=136)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/e5af681c-00bc-49de-b2ce-e7f738fdc6c6.png?resizew=379)
如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79516f18a7daf0ad467a48e16d0e65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79516f18a7daf0ad467a48e16d0e65f.png)
![](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/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79516f18a7daf0ad467a48e16d0e65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47d3270501173ad722523a7b91cea01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e09700a78d26bf865945ceec87bd94.png)
下面是该定理的证明过程(部分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa96c86a9085aeb7a57ce955200f0c80.png)
延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42774a918f52ac8aa8b1f5b78a676f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed609d8930e0b2135e77c79b8e0b2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24af3580af6754589e0df654ca6735f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840f793cf9a73e468427071e9dfecaee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d99c854e874161cd936d4d7848d4385e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ca70b1bc18e224ba94d873219a359d.png)
如图2,在图1(隐去
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df1a193f17a78036f3a63c735f79edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
如图2,动手连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9020059d62af7498039f091de6f005ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679165ed0b961fb0e8643fcdab64937b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1949518fc246fbd8426d08f701ade25d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd66f89184ca925f4575c26053decf2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be72ff5e7abb13db0fc8ccbb492732a.png)
![](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/2e42ab439ed525d1fd1de20bf921b831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2516c1f30bcef258b201be137b672fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f053a7a463cc1d4b5b866dda0f71dff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f65029da732ae715a88074e3298d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6c865065e08cd749ea659ce8163271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd66d053fad701617e39569eb47d444.png)
(1)观察发现:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3045155183b60255854bf010b457f115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16268d71c64f43aeeafac9900bdecfe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(2)请观察式子①和式子②,并利用任务(1)的结论,按照上面的证明思路,完成该定理证明的剩余部分.
您最近一年使用:0次
10 . 如图,已知点
是双曲线
在第一象限的分支上的一个动点,连接
并延长交另一分支于点
,以
为边作等边
,点
在第四象限.则点
的纵坐标随横坐标变化的函数解析式是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef854dfcbba9b7dedc1bc52f6332b011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/24c9d25a-c566-4919-82e4-a72972858aba.png?resizew=230)
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