1 . 已知动圆过定点
,且截
轴所得的弦长为4.
(1)求动圆圆心
的轨迹方程;
(2)若点
,过点
的直线交
的轨迹于
两点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf90f8358fa8cd9bc8c99ea48d9ae1a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7095e1d0e3e6be39a3ac68ad76bd9f26.png)
您最近一年使用:0次
2024-03-21更新
|
720次组卷
|
2卷引用:黑龙江省双鸭山市第三十一中学等校2024届高三第二次模拟数学试题
名校
解题方法
2 . 设抛物线
的准线为l,A、B为抛物线上两动点,
于
,定点
使
有最小值
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/f32f8a5e-ab97-41a3-a59b-f0f7f66fbb26.png?resizew=155)
(1)求抛物线的方程;
(2)当
(
且
)时,是否存在一定点T满足
为定值?若存在,求出T的坐标和该定值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf39f807af4ea7bec39fe04b60566c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f0ac21a3b9c3e7d11d1547217850b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31be0ce029f4205563bf67a73d55a143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/f32f8a5e-ab97-41a3-a59b-f0f7f66fbb26.png?resizew=155)
(1)求抛物线的方程;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941dcd189840d67264beaa7f973b87e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472393b18c7880e73b40e31fbe2d951c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bc8d143b8678e32e891a2cf552f4682.png)
您最近一年使用:0次
2022-12-04更新
|
1495次组卷
|
10卷引用:3.3.2 抛物线的简单几何性质【第三课】“上好三节课,做好三套题“高中数学素养晋级之路
(已下线)3.3.2 抛物线的简单几何性质【第三课】“上好三节课,做好三套题“高中数学素养晋级之路四川省成都市第七中学2022-2023学年高二上学期期中数学理科试题四川省成都市成都市第七中学2022-2023学年高二上学期期中数学文科试题四川省成都市树德中学2022-2023学年高二上学期期中考试数学(理)试题云南省大理市下关第一中学教育集团2022~2023学年高二上学期段考(二)数学试题(A卷)云南省下关第一中学2022-2023学年高二上学期段考(二)数学(A卷)试题辽宁省沈阳市东北育才双语学校2022-2023学年高二上学期期末数学试题(已下线)专题04 圆锥曲线经典题型全归纳(2)广西壮族自治区南宁市第三中学2023届高三模拟数学(理)试题(二)湖南省长沙市长郡中学2023-2024学年高二上学期期中数学试题
3 . 已知抛物线C:
(
)的焦点为F,直线
与C交于A,B两点,
.
(1)求C的方程;
(2)过A,B作C的两条切线交于点P,设D,E分别是线段PA,PB上的点,且直线DE与C相切,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e1bc08cc69d3d8e73b990f1236ed5c.png)
(1)求C的方程;
(2)过A,B作C的两条切线交于点P,设D,E分别是线段PA,PB上的点,且直线DE与C相切,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da715afe51a44ad2f044ccf61c313778.png)
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4 . 在①
;②
;③
面积的最小值为8,这三个条件中任选一个,补充在横线上,并解答下列问题.(若选择多个条件作答,则按第一个解答计分)
已知抛物线
的焦点为F,过点F的直线与该抛物线交于A,B两点,O为坐标原点,_____________.
(1)求抛物线的方程;
(2)点C在抛物线上,
的重心G在y轴上,直线
交y轴于点Q(点Q在点F上方).记
的面积分别为
,求T的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59411f424d59bc4de8f2b2e124fdbba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9520ae34d0893349c8e2a09dbb7943f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
已知抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
(1)求抛物线的方程;
(2)点C在抛物线上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75e3c33ea291d63a5fbb161e0806f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510317d708a6e4fef916cdf6901bc7b4.png)
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5 . 设O为坐标原点,直线
与抛物线C:
交于A,B两点,若
.
(1)求抛物线C的方程;
(2)若斜率为
的直线l过抛物线C的焦点,且与抛物线C交于D,E两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(1)求抛物线C的方程;
(2)若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ea907b820c999daced6c12a4f876fc.png)
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2023-11-03更新
|
655次组卷
|
5卷引用:黑龙江省哈尔滨市第九中学2023-2024学年高二下学期开学考试数学试卷
名校
解题方法
6 . 已知抛物线
的准线是
,直线
与抛物线
没有公共点,动点
在抛物线
上,过点
分别作直线
的垂线,垂足分别为
,且
的最小值为
.
(1)求抛物线
的方程;
(2)过
作两条不同的直线
,分别与抛物线
相交于点
与点
,且线段
的中点分别为
.若直线
的斜率之和为2,试问直线
是否经过定点?若经过定点,请求出定点坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebe6bf7fa7a4e946292cb8acf41042e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237c115d5b39d761e1cbcae031070b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94182731f9e580137d754f0823459161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a29b194f0420de3594df9207d712265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
7 . 已知动圆过定点
,且与直线
相切,其中
.
(1)求动圆圆心
的轨迹的方程;
(2)设
、
是轨迹
上异于原点
的两个不同点,直线
和
的倾斜角分别为
和
,当
、
变化且
,证明直线
恒过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4356a596535d4e905ae47e191940f34f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b64b91d079810d968b9ef63e3284c7af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ec866a38a23f014dee37ed4bda40ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-11-29更新
|
1404次组卷
|
3卷引用:3.3.2 抛物线的简单几何性质【第三课】“上好三节课,做好三套题“高中数学素养晋级之路
(已下线)3.3.2 抛物线的简单几何性质【第三课】“上好三节课,做好三套题“高中数学素养晋级之路2005年普通高等学校招生考试数学(文)试题(山东卷)辽宁省沈阳市第二中学2022-2023学年高三上学期12月月考数学试题
解题方法
8 . 已知抛物线
的焦点为F,直线
与C交于A,B两点,当
时,
.
(1)求抛物线C的方程;
(2)若直线
与抛物线C交于M,N两点,证明:由直线
,直线
及y轴围成的三角形为等腰三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a52ed056cec5b7ff6f6312af07b54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e788c32187ae2cc97aaa24da1d40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24575e857b1cb5261b05f262454b3e1a.png)
(1)求抛物线C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6baf60667c716c54e73db456604b5914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
您最近一年使用:0次
解题方法
9 . 已知抛物线
过点
(
).
(1)求C的方程;
(2)若斜率为
的直线过C的焦点,且与C交于A,B两点,求线段
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c972a29cc3347c42003c517e4edc08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)求C的方程;
(2)若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-07-08更新
|
653次组卷
|
7卷引用:专题05 抛物线8种常见考法归类(2)
(已下线)专题05 抛物线8种常见考法归类(2)广东省汕尾市2022-2023学年高二下学期期末数学试题(已下线)第24讲 抛物线的简单几何性质6种常见考法归类(1)(已下线)专题3.10 圆锥曲线的方程全章八类必考压轴题-2023-2024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)(已下线)第06讲 3.3.2抛物线的简单几何性质(1)(已下线)模块四 专题6 大题分类练(圆锥曲线的方程)基础夯实练(人教A)(已下线)第08讲:圆锥曲线(大题) (必刷7大考题+7大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)
22-23高二下·上海浦东新·阶段练习
10 . 已知平面曲线
满足:它上面任意一定到
的距离比到直线
的距离小1.
(1)求曲线
的方程;
(2)
为直线
上的动点,过点
作曲线
的两条切线,切点分别为
,证明:直线
过定点;
(3)在(2)的条件下,以
为圆心的圆与直线
相切,且切点为线段
的中点,求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d655ee6d4c2285b6f59652360862d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652c2cea7e7421065b84c3673aef18e9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb70fdf064b9193e506ca43f4672af56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)在(2)的条件下,以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18834eb93b2553bccfa11d20b704a4d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945e93c9f3515ded840de09a9ba81ce8.png)
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