名校
解题方法
1 . 根据抛物线的光学性质可知,从抛物线的焦点发出的光线经该抛物线反射后与对称轴平行,一条平行于对称轴的光线经该抛物线反射后会经过抛物线的焦点.如图所示,从
沿直线
发出的光线经抛物线
两次反射后,回到光源接收器
,则该光线经过的路程为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4a2b6903a43f3b11cafb03bc23f02a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f617b6bfb31dc4556a0e9f1f547164ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ee70f162a8e6d8b4da58b6189b0b33.png)
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899348862803968/2901325183606784/STEM/d388bd2d-de83-477e-b253-a8cf61237a3f.png?resizew=161)
您最近一年使用:0次
2022-01-24更新
|
783次组卷
|
12卷引用:河北省邯郸市十校联考2022届高三上学期期末数学试题
河北省邯郸市十校联考2022届高三上学期期末数学试题内蒙古通辽市2021-2022学年高三上学期期末考试数学(文)试题贵州省遵义市2021-2022学年高二上学期期末考试数学(理)试题贵州省遵义市2021-2022学年高二上学期期末考试数学(文)试题河北省石家庄市行唐县2022届高三上学期期末数学试题(已下线)高二上学期期末【常考60题考点专练】(选修一+选修二)-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)重庆市第八中学2021-2022学年高二下学期第一次月考数学试题青海省海东市2022届高考一模数学(理)试题青海省海东市2022届高考一模数学(文)试题安徽省宣城中学2023届高三原创模拟金卷(一)数学试题(已下线)专题3.3 抛物线(4类必考点)-2022-2023学年高二数学必考点分类集训系列(人教A版2019选择性必修第一册)(已下线)专题3.18 圆锥曲线的方程全章综合测试卷-提高篇-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)
2 . 抛物线有一条重要性质:从焦点发出的光线,经过抛物线上的一点反射后.反射光线平行于抛物线的轴.已知抛物线
,平行于
轴的光线在抛物线上点
处反射后经过抛物线的焦点
,在抛物线上点
处再次反射,又沿平行于
轴方向射出,则两平行光线间的最小距离为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2021-03-12更新
|
177次组卷
|
4卷引用:河北省邯郸市2020-2021学年高二上学期期末数学试题
河北省邯郸市2020-2021学年高二上学期期末数学试题上海市张堰中学2021届高三下学期第一次阶段考试数学试题江西省上饶市横峰中学2020-2021学年高二下学期第一次月考数学(文)试题(已下线)模块12 圆锥曲线-2022年高考数学一轮复习小题多维练(上海专用)
名校
解题方法
3 . 平面内一动点D到直线
的距离比D到点
的距离小1,
(1)求动点D的轨迹C的方程;
(2)已知动直线l过点
,交轨迹C于A,B两点,坐标原点O为
的中点,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae045f9b7daebb9f15b8769575f62484.png)
(1)求动点D的轨迹C的方程;
(2)已知动直线l过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6bc1ce0bb051d00c6c75d51a845926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe2381b2935a320e50e12c573685206.png)
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4 . 已知抛物线
,点
,
,点
在抛物线上,则满足
为直角三角形的点
的个数有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb9603390e28948abd2e3cd96e1720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888a6b10db4d81e5d2ba969fb576bd78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebf09886d78142f483e163e0919dc50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.2 | B.4 | C.6 | D.8 |
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解题方法
5 . 平面上动点
到定点
的距离比动点
到直线
的距离小1.记
的轨迹为曲线
.
(1)求曲线
的方程;
(2)若曲线
上相异两点
,
关于直线
对称,且
,求实数
的值.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d733aa63c362191db9efb959053fcf3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
6 . 已知直线
与抛物线
相切于点
,且与
的准线相交于点
,
为
的焦点,连接
交
于另一点
,则
面积的最小值为______ ;若
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c969fb12619bb081f7d0483ea2b7db0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb88bd08cff4ffbe4d832153c99747bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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2021-01-28更新
|
271次组卷
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3卷引用:山东省济南市2020-2021学年高三上学期期末数学试题
7 . 直线l与抛物线
相交于A,B两点,线段AB的中点为M,点P是y轴左侧一点,若线段PA,PB的中点都在抛物线上,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
A.PM与y轴垂直 | B.PM的中点在抛物线上 |
C.PM必过原点 | D.PA与PB垂直 |
您最近一年使用:0次
2021-01-27更新
|
530次组卷
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3卷引用:安徽省蚌埠市2020-2021学年高二上学期期末理科数学试题
安徽省蚌埠市2020-2021学年高二上学期期末理科数学试题江西省宜春市2021届高三高考数学(理)模拟试题(已下线)专题27 圆锥曲线点差法必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)
名校
8 . 某校运会上进行无人机飞行表演,飞行水平距离总长60米(即线段
长度为60米).飞行轨迹如图所示,起点
离地30米(
),最低点
离地10米,从起点飞到最低点水平距离经过20米.最高点
离地50米,从起点到最高点的轨迹为开口向上的抛物线的一段(端点为
,
),达到最高点后的轨迹为线段
,终点N与
点等高.建立合适平面直角坐标系,并求
![](https://img.xkw.com/dksih/QBM/2021/1/19/2639471875948544/2641732497301504/STEM/e346186f-509c-4ca1-b5ca-34420546f1fa.png?resizew=265)
(1)线段
所在直线与水平线(地面)的夹角的正切值;
(2)在与
等高的
处有摄像机拍摄,
与
的水平距离为10米,为确保始终拍到无人机,求拍摄视角
的最小值.(精确到
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2289faaaa3296b1a5826ab6c3cdf5a68.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2021/1/19/2639471875948544/2641732497301504/STEM/e346186f-509c-4ca1-b5ca-34420546f1fa.png?resizew=265)
(1)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
(2)在与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c74a88e12936aaa3518764d5fb5192.png)
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名校
解题方法
9 . 过抛物线
的焦点
作直线与抛物线在第一象限交于点
,与准线在第三象限交于点
,过点
作准线的垂线,垂足为
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bb4c004df1d9dd02be20156e2fcf97.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96035c7551cc5b7223cd10ccc507ebd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52bb0f4140073a47e45c5093be46f1a9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
10 . 设抛物线
的焦点为
,
为抛物线上的两个动点,且满足
,过弦
的中点
作抛物线准线的垂线
,垂足为
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc215d4797ad7415f197ed1972704321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c683d0f5034025be78bb6be865c8368a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-01-09更新
|
507次组卷
|
6卷引用:黑龙江省哈尔滨市第六中学2020-2021学年高二上学期期末考试数学(理)试题