名校
解题方法
1 . 在平面直角坐标系
中,
是直角三角形,
,
,点
,
分别在
轴和
轴上运动,点
关于
的对称点为
.
(1)求动点
的轨迹方程;
(2)若过点
的直线
与点
的轨迹交于
,
两点,
,求直线
,
的斜率之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b321185ca990a70242f952e15afd6db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770115c673b16a06eebd4e460b725fb4.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/ac047e91852b91af639feec23a9598b2.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a676c8dc56e5ade5c24eb0fefe676c92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
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2023-12-26更新
|
460次组卷
|
4卷引用:江西省吉安市多校联考2023-2024学年高二下学期3月月考数学试题
江西省吉安市多校联考2023-2024学年高二下学期3月月考数学试题安徽省亳州市涡阳县蔚华中学2023-2024学年高二上学期第三次月考数学试题(已下线)专题03 圆锥曲线题型全归纳(九大考点)-【寒假自学课】2024年高二数学寒假提升学与练(人教A版2019)(已下线)微考点6-6 圆锥曲线中斜率和积与韦达定理的应用
2 . 石城永宁桥,省级文物保护单位,位于江西省赣州市石城县高田镇.永宁桥建筑风格独特,是一座楼阁式抛物线形石拱桥.当石拱桥拱顶离水面1.6m时,水面宽6.4m,当水面下降0.9m时,水面的宽度为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/3156dca8-f158-4c39-848d-984c318f9662.png?resizew=356)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/3156dca8-f158-4c39-848d-984c318f9662.png?resizew=356)
A.7m | B.7.5m | C.8m | D.8.5m |
您最近一年使用:0次
名校
3 . 某城市有一块不规则的空地(如图),两条直边
,曲边
近似为抛物线的一部分,该抛物线的对称轴正好是直线
.该城市规划部门计划利用该空地建一座市民活动中心,该中心的基础建面是一个矩形
在边
上,
在边
上,
在曲边
上,为使建面
最大,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e08831f4fdcd519fed4c7359c1248b.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db64ae23d3e7bd4b0a7e1a7742238c9.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/7002f54f7ac9e7f283a257dd75394333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e08831f4fdcd519fed4c7359c1248b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/2/1fc78c2e-6071-4ab1-9414-8b0e2d8c84fc.png?resizew=173)
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2023-06-01更新
|
605次组卷
|
4卷引用:江西师范大学附属中学2023届高三三模考试数学(理)试题
江西师范大学附属中学2023届高三三模考试数学(理)试题江西师范大学附属中学2023届高三三模考试数学(文)试题(已下线)考点巩固卷08 利用导数研究函数的单调性、极值和最值( 十一大考点)(已下线)专题16 函数与不等式解图形最值问题
2023·江西·二模
4 .
北京冬奥会顺利召开,滑雪健将谷爱凌以
金
银的优秀成绩书写了自己的传奇,现在她从某斜坡上滑下,滑过一高度不计的滑板后落在另一斜坡上,若滑板与水平地面夹角的正正切值为
,斜坡与水平地面夹角的正正切值为
,那么她最后落在斜坡上速度与水平地面夹角的正正切值为( )(不计空气阻力和摩擦力)
![](https://img.xkw.com/dksih/QBM/2023/4/8/3212347224555520/3213243248615424/STEM/c699ee5064bf432dac4217659b054ca9.png?resizew=228)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d01dd350dc95f42f1883e0cc7aae084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://img.xkw.com/dksih/QBM/2023/4/8/3212347224555520/3213243248615424/STEM/c699ee5064bf432dac4217659b054ca9.png?resizew=228)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
5 . “米”是象形字.数学探究课上,某同学用拋物线和
构造了一个类似“米”字型的图案,如图所示,若抛物线
,
的焦点分别为
,
,点
在拋物线
上,过点
作
轴的平行线交抛物线
于点
,若
,则
( )
A.2 | B.3 | C.4 | D.6 |
您最近一年使用:0次
2023-03-24更新
|
1162次组卷
|
9卷引用:江西省南昌市2023届高三第一次模拟测试数学(理)试题
名校
解题方法
6 . 过坐标原点
作圆
的两条切线,设切点为
,直线
恰为抛物
的准线.
(1)求抛物线
的标准方程;
(2)设点
是圆
上的动点,抛物线
上四点
满足:
,设
中点为
.
(i)求直线
的斜率;
(ii)设
面积为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d499a21e40eecada13c79efd20245b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5b98ea929dbf828baad9629255d195.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63368fb5c4feebe59c81bd5c90d8eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eada7f7629bcc6e73f95328d9d0139cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(i)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1ab6c10bc0a8bfbdc3b4824c2de1d1.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04e30d5827f2120d997997e4e31ba17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2023-02-19更新
|
4428次组卷
|
5卷引用:江西省南昌市第二中学2023-2024学年高二下学期期中考试数学试卷
江西省南昌市第二中学2023-2024学年高二下学期期中考试数学试卷湖北省武汉市2023届高三下学期二月调研数学试题安徽省阜阳市颍上第一中学2022-2023学年高二下学期第一次月考数学试题重庆市长寿中学2022-2023学年高三下学期3月月考数学试题(已下线)上海市华东师范大学第二附属中学2024届高三上学期期中数学试题
名校
解题方法
7 . 首钢滑雪大跳台是冬奥史上第一座与工业旧址结合再利用的竞赛场馆,它的设计创造性地融入了敦煌壁画中飞天的元素,建筑外形优美流畅,飘逸灵动,被形象地称为雪飞天.中国选手谷爱凌和苏翊鸣分别在此摘得女子自由式滑雪大跳台和男子单板滑雪大跳台比赛的金牌.雪飞天的助滑道可以看成一个线段
和一段圆弧
组成,如图所示.假设圆弧
所在圆的方程为
,若某运动员在起跳点
以倾斜角为
且与圆
相切的直线方向起跳,起跳后的飞行轨迹是一个对称轴在
轴上的抛物线的一部分,如下图所示,则该抛物线的轨迹方程为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/a86cfb46-a49e-4a49-8d0b-6df1d82f436f.png?resizew=474)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba9243b35b9abb5d87efa0a9b463f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba9243b35b9abb5d87efa0a9b463f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4486de9ab5f443ae99ab433301a536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/a86cfb46-a49e-4a49-8d0b-6df1d82f436f.png?resizew=474)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2022-05-25更新
|
1954次组卷
|
7卷引用:江西省南昌市2022-2023学年高二上学期末质量检测数学模拟试题
江西省南昌市2022-2023学年高二上学期末质量检测数学模拟试题安徽省合肥市第一中学2022届高三下学期最后一卷文科数学试题(已下线)专题26 求动点轨迹方程 微点7 求动点轨迹方程综合训练(已下线)专题37 求曲线的轨迹方程-4(已下线)考向34 抛物线(重点)广东省珠海市第一中学2023届高三下学期5月阶段性考试一数学试题(已下线)专题14 抛物线-1
解题方法
8 . 已知抛物线
,焦点为
,过
作动直线
交抛物线
于
两点
,过
作抛物线
的切线
,过
作直线
的平行直线
交
轴于
,设线段
的垂直平分线为
,直线
的倾斜角为
.已知当
时,
.
(1)求抛物线
的方程;
(2)证明:直线
过
轴上一定点,并求该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/4daf40bad1cc89311930cce356672354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb31cb079c66cb83d4ef0a3310f8662.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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f331c3d96c5812a620e326373747eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2913f8d730167b2bc9bbbbf809de4b1a.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
您最近一年使用:0次
解题方法
9 . 已知
是抛物线
上一点,
是
轴上的点,以
为圆心且过点
的圆与
轴分别交于点
、
,且当圆
与
轴相切时,
到抛物线焦点的距离为
.
(1)求抛物线
的标准方程;
(2)设线段
、
长度分别为
、
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/5963abe8f421bd99a2aaa94831a951e9.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/a4b8503f4706b8321e4e79a87eadea84.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
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2021·全国·模拟预测
10 . 过原点O的直线与拋物线C:
(
)交于点A,线段OA的中点为M,又点
,
.在下面给出的三个条件中任选一个填在横线处,并解答下列问题:
①
,②
;③
的面积为
.
(1)______,求拋物线C的方程;
(2)在(1)的条件下,过y轴上的动点B作拋物线C的切线,切点为Q(不与原点O重合),过点B作直线l与OQ垂直,求证:直线l过定点.
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a85af9db2d0ff7bf57aea3a1a94be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a69f6a208dd6671c46271b78430d79b.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2fa186e33cebc902d8922c63e3ade0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7ca98e754e7bc28ad381711b680673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225c0723cc3e08112fde8a02051997d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec978eb43bc4f9e7df83b0d0195dcda.png)
(1)______,求拋物线C的方程;
(2)在(1)的条件下,过y轴上的动点B作拋物线C的切线,切点为Q(不与原点O重合),过点B作直线l与OQ垂直,求证:直线l过定点.
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
2021-12-30更新
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560次组卷
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4卷引用:江西省丰城市第九中学2021-2022学年高二上学期期末数学(文)试题
江西省丰城市第九中学2021-2022学年高二上学期期末数学(文)试题(已下线)2022届高三普通高等学校招生全国统一考试数学信息卷(六)(已下线)解密16 抛物线方程(分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(新高考专用)2023版 北师大版(2019) 选修第一册 名师精选卷 高考水平模拟性测试(二)