名校
解题方法
1 . 已知抛物线
的焦点为F,抛物线C上存在n个点
,
,
,
(
且
)满足
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5932fd1fed3afdc0946e7d218168877.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2022-03-30更新
|
3477次组卷
|
12卷引用:广东省2022届高三一模数学试题
广东省2022届高三一模数学试题湖北省襄阳市第五中学2022届高三下学期适应性考试(三)数学试题湖南省长沙市长郡中学2022届高三下学期高考前冲刺(一)数学试题河北省2022届高考临考信息(预测演练)数学试题(已下线)必刷卷05-2022年高考数学考前信息必刷卷(新高考地区专用)(已下线)2022年高考考前20天终极冲刺攻略(三)【数学】(新高考地区专用)(5月29日)广东省汕头市金山中学2021-2022学年高二下学期期中数学试题(已下线)考点22 抛物线-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)(已下线)江苏省南通市如皋市2022-2023学年高三上学期9月诊断测试数学试题(已下线)广东省2022届高三一模数学试题变式题11-16浙江名校联盟2022-2023学年高二下学期期中联考数学试题(B卷)浙江省绍兴市第一中学2022-2023学年高三上学期10月月考数学试题
名校
解题方法
2 . 已知
,
是经过抛物线
焦点
的互相垂直的两条弦,若
的倾斜角为锐角,
,
两点在
轴上方,则下列结论中一定成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() |
B.设![]() ![]() ![]() |
C.若直线![]() ![]() ![]() |
D.![]() |
您最近一年使用:0次
3 . 已知抛物线
,焦点为
,过
作两条关于直线
对称的直线分别交
于
两点.
(1)判断直线
的斜率是否为定值?若是,求出定值;若不是,请说明理由.
(2)若
三点在抛物线
上,且满足
,证明
三个顶点的横坐标均小于2.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75d41bd21b19b7e1ba41d904104a9229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfb23a9e07213cb76990dbedfc7feca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89b6e4f0c8497a9d4e6b887dc4fda0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804ea12070cefc8ca3bde7697c82ad6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
您最近一年使用:0次
4 . 曲线
上动点
与
构成
,若
,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67d93773ed34cfe79fd47025c9dac1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51296b06e4f0ac74bea949ce2d9faa6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ac378e1dd219184c4a0d722acb10f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2024-02-23更新
|
968次组卷
|
2卷引用:广东2024届高三数学新改革适应性训练三(九省联考题型)
解题方法
5 . 从抛物线的焦点发出的光经过抛物线反射后,光线都平行于抛物线的轴,根据光路的可逆性,平行于抛物线的轴射向抛物线后的反射光线都会汇聚到抛物线的焦点处,这一性质被广泛应用在生产生活中.如图,已知抛物线
,从点
发出的平行于y轴的光线照射到抛物线上的D点,经过抛物线两次反射后,反射光线由G点射出,经过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/15/90005741-f392-43ed-8285-cc57749395c1.png?resizew=158)
(1)求抛物线C的方程;
(2)已知圆
,在抛物线C上任取一点E,过点E向圆M作两条切线EA和EB,切点分别为A、B,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a44d91ee49191f7b55bafad8f65dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51ce47eaa3ad3a466b993f84ac5ebe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d82ec141c8e84ac00891f48577052e4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/15/90005741-f392-43ed-8285-cc57749395c1.png?resizew=158)
(1)求抛物线C的方程;
(2)已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e933036a30cf7839de1ddb9c64bf21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53aec2ef0bbe7a2d482aa35b9826ec6.png)
您最近一年使用:0次
6 . 设
为平面上两点,定义
、已知点P为抛物线
上一动点,点
的最小值为2,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
_________ ;若斜率为
的直线l过点Q,点M是直线l上一动点,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093c6d5bcaa69cea79b24688f5d1bd97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50061a63fdbd8394471c07f333d9fec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314837d3a10726c5f83528f791d20020.png)
您最近一年使用:0次
2024-06-04更新
|
863次组卷
|
4卷引用:山东省枣庄市2024届高三三调数学试题
山东省枣庄市2024届高三三调数学试题山东省青岛市2024届高三下学期第二次适应性检测数学试题(已下线)山东省济南市2024届高三下学期5月适应性考试(三模)数学试题湖北省武汉市汉铁高级中学2024届高考数学考前临门一脚试卷
7 . 如图,已知四边形
的四个顶点都在抛物线
上,且A,B在第一象限,
轴,抛物线在点A处的切线为l,且
.
的斜率分别为k和
,求
的值;
(2)P为
与
的交点,设
的面积为
,
的面积为
,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a20e3b66f99144a013bba3c2c00a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7ce5d5cc777ef4d5b890cc9cbb70b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae076e151c24084f1ca2ca502dede95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e08d5c04f0431fb57b33a01717b599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35cc2384c66ee5559a9e5ec40dd75669.png)
(2)P为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2718f4bc0d51cb2a6c91ad7069954550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
8 . 已知点
和点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9395c9b4769c1ae5fbfe5fd34771ac46.png)
之间的距离为2,抛物线
经过点N,过点M的直线l与抛物线C有两个不同的交点A,B,点E,F分别在直线
,
上,且
,
(O为坐标原点).
(1)求直线l的倾斜角的取值范围;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25e326fdf9e5456f48e8a99a069f379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9395c9b4769c1ae5fbfe5fd34771ac46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9237a77905f07b4b99fee49c7e2abb53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c023f4b501684abd869b36d6e6c7f21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1de080f965097aa7e1dd9e21fd8554a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9239ee786a3fe3aabd17ad5c61406.png)
(1)求直线l的倾斜角的取值范围;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,已知点
在半圆
:
上一点,过点P作抛物线C:
的两条切线,切点分别为A,B,直线AP,BP,AB分别与x轴交于点M,N,T,记
的面积为
,
的面积为
.
![](https://img.xkw.com/dksih/QBM/2022/2/16/2917780834074624/2918913037582336/STEM/69b2636d-dd93-4c06-b114-72d6a5764755.png?resizew=182)
(1)若抛物线C的焦点坐标为(0,2),求p的值和抛物线C的准线方程:
(2)若存在点P,使得
,求p的取值范围.
![](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/6f2c1a1c868218dd0be4e77ca9cfe84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f9cbd5fce2c4819aadefcf10dcd4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd68201c2f21edf7575166ce1ef82ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://img.xkw.com/dksih/QBM/2022/2/16/2917780834074624/2918913037582336/STEM/69b2636d-dd93-4c06-b114-72d6a5764755.png?resizew=182)
(1)若抛物线C的焦点坐标为(0,2),求p的值和抛物线C的准线方程:
(2)若存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506c25a883f7d0e2342419e1e9f6b142.png)
您最近一年使用:0次
2022-02-18更新
|
1258次组卷
|
3卷引用:四川省成都市石室中学2022届高三专家联测卷(五)数学(理)试题
10 . 已知抛物线
的焦点
在
轴的正半轴上,顶点是坐标原点
是圆
与
的一个交点,
是
上的动点,且
在
轴两侧,直线
与圆
相切,线段
线段
分别与圆
相交于点
.
(1)求
的方程;
(2)
的面积是否存在最大值?若存在,求使
的面积取得最大值的直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a9014cca417cae993ed524c0a7e367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56648a303009f944e1a9983c3f62c7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d180e724b66d757b466e953a3f7abb17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/919eab7a4cd4e467fd50d301a03e70ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次