1 . 已知函数
,若数列
的各项由以下算法得到:
①任取
(其中
),并令正整数
;
②求函数
图象在
处的切线在
轴上的截距
;
③判断
是否成立,若成立,执行第④步;若不成立,跳至第⑤步;
④令
,返回第②步;
⑤结束算法,确定数列
的项依次为
.
根据以上信息回答下列问题:
(1)求证:
;
(2)是否存在实数
使得
为等差数列,若存在,求出数列
的项数
;若不存在,请说明理由.参考数据:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71601a0573a3d598bea17f989570fd59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
①任取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd3ecf27b4de4d36c92c072b17a2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
②求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d896b1e6cadb21a23acb227c18b238b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5b6045219ea4527202ab131bb2e.png)
③判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11ef454b69c4ce4fd731b6f2ec13d70.png)
④令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2583433b021057d8bf772e20f9420a.png)
⑤结束算法,确定数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a94ba3f4906ba526f9f6676540a99b6.png)
根据以上信息回答下列问题:
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72bedf7ef340c4cb9522106f53ef5f37.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb6e83865e833f866807dfbced86dc9.png)
您最近一年使用:0次
名校
解题方法
2 . 已知点
是圆
的动点,过
作
轴,
为垂足,且
,
,记动点
,
的轨迹分别为
,
.
(1)证明:
,
有相同的离心率;
(2)若直线
与曲线
交于
,
,与曲线
交于
,
,与圆
交于
,
,当
时,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8efd7b690113cfc851401e1540ac1132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb8f6c438fe1fc036c92ccd3fa8465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5d3e8de22b4cadd3aacc6b955dbcd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b62adcc036ff4122e642b506d46c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6824ebd7ee7da0bed69bd761dbb762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.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/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](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/457e56d8aa132b2aad38ecf7e45f1cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34d2c05dd46ab2ac99d32be44a1465c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3c6876c328f7d7a08515e78fdba136.png)
您最近一年使用:0次
2024-02-28更新
|
348次组卷
|
2卷引用:四川省绵阳市东辰学校2024届高三下学期第二学月考试数学(理科)试题
2024·四川成都·模拟预测
名校
3 . 已知
R,
为坐标原点,函数
.下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526c6e33166cdaadce9d0226b67642c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbcd92e2ade8848dc15d7235cab5647.png)
A.当![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
4 . 如图,抛物线
与
轴负半轴交于点
,与
轴正半轴交于点
,与
轴交于点
,
.
(1)求抛物线的解析式;
(2)设
是第四象限内抛物线上的点,连接
.
①求点
的坐标;
②连接
,若点
是抛物线上不重合的两个动点,在直线
上是否存在点
(点
按顺时针方向排列,点
按顺时针排列),使得
且
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7b50361cfc74af7a250e058f8c0c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2a988dc9f03fffcd8acb720d706e9c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/9/72af2cf6-46f5-4831-b8b4-a2f336555c3e.png?resizew=278)
(1)求抛物线的解析式;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d928a3bcf169c67c51a9006f6d29dc67.png)
①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
②连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd17f1c6f82c15d141ef817a636af90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dac152e5e7d8f9549fbc04c1d42bbfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/332ff50725ece7eb1ac731431768289b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6556d1de4797ef7549a8d983f2da99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877260f1b1ff5dda376e1cefb9f5e9bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
5 . 如图,在平面直角坐标系中,直线
经过点
,与
轴正半轴交于
点,与反比例函数
交于点
,且
轴交反比例函数
于点
.
(1)求
的值;
(2)如图1,若点
为线段
上一点,设
的横坐标为
,过点
作
,交反比例函数
于点
.若
,求
的值.
(3)如图2,在(2)的条件下,连接
并延长,交
轴于点
,连接
,在直线
上方是否存在点
,使得
与
相似(不含全等)?若存在,请求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87aba319e62dd0fe1c2db30759a8ded7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d57173ef4cd72eb270686875dfd623.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/03517310ea1e913f709753592ac65ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e03375e9fa2a949058828f5a5ecce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03517310ea1e913f709753592ac65ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/8e09502e-c5ba-434f-bcf3-b16fb8f38112.png?resizew=477)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a389234de46c9654804bada595264b.png)
(2)如图1,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d64d857c9e44dc69b19e1587e2aa677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03517310ea1e913f709753592ac65ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f72423bf19b975448fd2a0eb4b4cbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)如图2,在(2)的条件下,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4e5962cfb17195352c899ddcd1650f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0526c0ac1d69705e031d1dbf95dd5220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
您最近一年使用:0次
6 . 设函数
(e为自然对数的底数),函数
与函数
的图象关于直线
对称.
(1)设函数
,若
时,
恒成立,求m的取值范围;
(2)证明:
与
有且仅有两条公切线,且
图象上两切点横坐标互为相反数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a903745cd2cb536443d07579b606ece5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c013c0ea4c429c9c553bba2ac9e86061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e10dce73bdc1d522ae7cb34805ed3d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6dd803c2811a3dfeebb65651153f2f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2024-01-08更新
|
525次组卷
|
2卷引用:四川省南充市2024届高三一模数学(理)试题
名校
解题方法
7 . 设函数
,
.
(1)①当
时,证明:
;
②当
时,求
的值域;
(2)若数列
满足
,
,
,证明:
(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df075cd20f79486d88d80ee12fc897d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5883f63cdc68865d41cc935b7b39557d.png)
(1)①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cdde751120c6deab563a6f7f8cf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffa28c7f519c1c85c0a3cad23b2e6cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ebb32ddcd84417fc992dad3ccba8894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adfbda63ad7cfeb044819141f1924598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
您最近一年使用:0次
2023-12-30更新
|
1078次组卷
|
4卷引用:四川省成都市第七中学2024届高三上学期期末数学(理)试题
(已下线)四川省成都市第七中学2024届高三上学期期末数学(理)试题重庆市育才中学、万州高级中学及西南大学附中2024届高三上学期12月三校联考数学试题广东省广州市华南师大附中2024届高三上学期大湾区数学预测卷(一)(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编
名校
解题方法
8 . 已知,椭圆的面积为
(其中,
为椭圆的长半轴长,
为椭圆的短半轴长).若椭圆
:
的左、右焦点分别为
,
,过
的直线与
交于
,
两点,直线
与
的另一交点为
(
,
,
均不与
顶点重合),
的周长为8,
的面积为
.
(1)求
的标准方程;
(2)
为原点,记直线
,
的斜率分别为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30489cd9c57a2c6283e0fc36129728c.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0407e1f5977d2cb46d362e8362c8816f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95cefb160c373407a49e3a8aee1a228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023037c7a3e31ba698c39f9b52db2515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5464bc1d5c3cf98043eac02a2fc66a55.png)
您最近一年使用:0次
2023-12-13更新
|
463次组卷
|
2卷引用:四川省达州市普通高中2024届高三上学期第一次诊断性测试数学试题(理科)
9 . 已知
,则在下列关系①
;②
;③
;④
中,能作为“
”的必要不充分条件的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd00e2f6802c99fb624aa77ebe17d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72f0a62b1a8614acae64570d8bf1170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b973e2ec0d256343c57ce0c3cd80ab2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65eb4d879e3e80d3195b56b303e331c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485a2d99320384a0857b00ce9ab9e990.png)
A.1个 | B.2个 | C.3个 | D.4个 |
您最近一年使用:0次
2023-11-11更新
|
688次组卷
|
2卷引用:四川省成都市第七中学2023-2024学年高三上学期期中考试理科数学试题
10 . 某数学兴趣小组运用《几何画板》软件探究
型抛物线图象.发现:如图1所示,该类型图象上任意一点M到定点
的距离
,始终等于它到定直线
上的距离
(该结论不需要证明),他们称:定点F为图象的焦点,定直线l为图象的准线,
叫做抛物线的准线方程.其中原点O为
的中点,
例如,抛物线
,其焦点坐标为
,准线方程为
.其中
.
(1)【基础训练】请分别直接写出抛物线
的焦点坐标和准线l的方程;
(2)【技能训练】如图2所示,已知抛物线
上一点P到准线l的距离为6,求点P的坐标;
(3)【能力提升】如图3所示,已知过抛物线
的焦点F的直线依次交抛物线及准线l于点
,若
求a的值;
(4)【拓展升华】古希腊数学家欧多克索斯在深入研究比例理论时,提出了分线段的“中末比”问题:点C将一条线段
分为两段
和
,使得其中较长一段
是全线段
与另一段
的比例中项,即满足:
,后人把
这个数称为“黄金分割”,把点C称为线段
的黄金分割点.如图4所示,抛物线
的焦点
,准线l与y轴交于点
,E为线段
的黄金分割点,点M为y轴左侧的抛物线上一点.当
时,求出
的面积值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45848d377cad2507fe6846d0882005e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1902e0111df0c03db02b5b44de18d020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8aed33984ccc91282d8a1c2be27cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be4f48d2f5b404bc554ce3ce26f2b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4418c0618a712877287ca49a222c07f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83f1f880e5ffbff036953acaca90c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b513c9a9f66302b497b46e5066f3ef03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafae84e7fe39dc5b694c39405201d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004cf3e8335136acc770de0c525cae47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5414f69b3282754397a185003db125a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0cfa5ca97d21f418606d449ab48540.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/9/c720cb40-587d-44b2-9b7e-17d573d2f9b8.png?resizew=606)
(1)【基础训练】请分别直接写出抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108c18cb76d7d34b05c991a644c8b136.png)
(2)【技能训练】如图2所示,已知抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce21531a886c50568b75fd4278f15dcf.png)
(3)【能力提升】如图3所示,已知过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45848d377cad2507fe6846d0882005e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa1359e6a95a7b27d60eeafd9df9d07.png)
(4)【拓展升华】古希腊数学家欧多克索斯在深入研究比例理论时,提出了分线段的“中末比”问题:点C将一条线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dfed575260fb066685a46ce7d91f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d393bb07b7140905b85f550519de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5421a28dc3675ae20190d6090793246e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dbb54aea6f3f59305b5c679f59bd08.png)
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