名校
解题方法
1 . 已知点
,直线
,动圆过点F且与直线l相切,动圆圆心轨迹为曲线
.
(1)求曲线
的方程;
(2)已知定点
,过点P的直线m交曲线C与M,N两点.
①若直线
与直线l交于点H,求
的最小值;
②在y轴上是否存在与点P不同的定点Q,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2347bec7975dab2b8bce2fd19b1237d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42502a5730e1930d77d7100d1e34707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0d26df529bbd8953f127102885f54e.png)
②在y轴上是否存在与点P不同的定点Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28390341f43e405f91454b05e2f406d1.png)
您最近一年使用:0次
解题方法
2 . 已知点
是直线
上一动点,定点
,过点
作直线
的垂线
与线段
的中垂线交于点
,动点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
的直线与曲线
交于
两点,且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b556b1a9944719cf423e90f8df16c773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609ade7633b9b03768ad9174b50c8742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
名校
解题方法
3 . 已知抛物线
的焦点
在
轴的正半轴上,点
在物物线内,若抛物线
上一动点
到
两点距离之和的最小值为4.
(1)求抛物线
的焦点坐标和准线方程;
(2)直线
过抛物线
的焦点
且倾斜角为
,并与抛物线
相交于
两点,求弦
的长度.
![](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/ab748cf5e6a17272677d0e9ae4d9588b.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/10d8348c89c6f13053325f4e1c62e29a.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](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/a0ed1ec316bc54c37c4286c208f55667.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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4 . 一青蛙从点
开始依次水平向右和竖直向上跳动,其落点坐标依次是
,(如图,
的坐标以已知条件为准),
表示青蛙从点
到点
所经过的路程.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/220d0549-124f-4dc9-b590-7ce2b6b0a176.png?resizew=157)
(1)点
为抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
准线上一点,点
,
均在该抛物线上,并且直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
经过该抛物线的焦点,证明
;
(2)若点
要么落在
所表示的曲线上,要么落在
所表示的曲线上,并且
,试写出
(不需证明);
(3)若点
要么落在
所表示的曲线上,要么落在
所表示的曲线上,并且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f5d00375f8083ff14dcf3745e4268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801c40c4b1b8b4155ccf08fc8df59342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f5d00375f8083ff14dcf3745e4268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/220d0549-124f-4dc9-b590-7ce2b6b0a176.png?resizew=157)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f5d00375f8083ff14dcf3745e4268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75ed10db4b9747a4b6d865b774f6b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfbb8b3c14e9617655321cab31acebc.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5661e7739636a3ff1479ab6a807d19b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0379cdb1fbe207a32568a978947fa41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e53542ad942e269a580a4dc7cc6fef.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf11327fc262b1351099455f6b9eed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02fa322f632dcd72048918b616511ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d55d2201d4d9aa7846b17a249ac528b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de918291423d4f2126ac8cc7d4b9edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772e1830de8a5b2bede8f5614d93a1d2.png)
您最近一年使用:0次
2024高三·全国·专题练习
5 . 在平面直角坐标系
中,点
到点
的距离等于点
到直线
的距离,记动点
的轨迹为
.求
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c41b2f7ca11db3aaea46c69286adbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
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2024·全国·模拟预测
解题方法
6 . 已知,点
分别是抛物线
的焦点与曲线上一动点,点
在抛物线上方,且
的周长最小值为
.
的方程;
(2)点
是抛物线上的动点,点
是点
处抛物线切线的交点,若
的面积等于32,线段
为圆
的直径,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d945b17623cd01fa90180c4d4fca91f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b1a27a8413f67d9f97785d9889e4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131ebfee8d3fd5d0c4d3b20012e232f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374cdec65a41dc616f6f099551880d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c8a7fc100c019e54242d3c323aba8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e265ce107592c375b78007107a9c00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99e568a7823999b05efcf80dc83be2b.png)
您最近一年使用:0次
7 . 已知动点P与定点
的距离等于点P到
的距离,设动点P的轨迹为曲线C.直线l与曲线C交于A,B两点,
(O为坐标原点).
(1)求曲线C的标准方程;
(2)求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(1)求曲线C的标准方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaceb8d6c6927e14d9ac7a557a2b11d.png)
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8 . 在平面直角坐标系
中,动点
到点
的距离与到
轴的距离之差等于1,记动点
的轨迹为
.
(1)求
的方程;
(2)设点
在
上,证明:直线
与
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af28d36abd098e090fa97da7dad181a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/398615228fc02ece024ee61774ce6000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036dee05f70ef2755be02545d53ccc9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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9 . 在
中,
的对边分别为
(其中
为定值),以
所在直线为
轴,
的垂直平分线为
轴建立直角坐标系(如图),请你给出适当的条件,求出顶点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23beb7fa35ed321584f95c7507b8b78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/95a4cb9c-ae1b-4ab2-97cd-3da35b044d71.png?resizew=165)
您最近一年使用:0次
名校
解题方法
10 . 已知动圆
过定点
,且与直线
相切.
(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
的斜率分别为
,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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30c084de07c0c84de9348cfa688088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2020-03-22更新
|
391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安徽省六安市舒城中学2019-2020学年高二上学期期末数学(理)试题江西省南昌市第十中学2020-2021学年高二上学期期中考试数学(文科)试题