解题方法
1 . 已知
是抛物线
上不同于原点
的两点,点
是抛物线
的焦点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/159a2d4945049c5a8f525f18763eba91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.点![]() ![]() |
B.![]() |
C.若![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() |
您最近一年使用:0次
2 . 过直线
上一点
作拋物线
的两条切线,设切点分别为
,记
是线段
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b556b1a9944719cf423e90f8df16c773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0261104a7c308433a0c0508ff20ea29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.直线![]() |
B.直线![]() |
C.线段![]() |
D.以线段![]() |
您最近一年使用:0次
2023-02-12更新
|
683次组卷
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4卷引用:辽宁省本溪市高级中学2023-2024学年高三上学期高考适应性测试(一)数学试题
辽宁省本溪市高级中学2023-2024学年高三上学期高考适应性测试(一)数学试题(已下线)考点20 常用的二级结论的应用 2024届高考数学考点总动员【练】浙江省绍兴市嵊州市2023届高三下学期2月学业质量调测数学试题江西省赣州市第四中学2024届高三上学期开学考试数学试题
名校
3 . 已知动圆Q过点
,且与直线
相切,记动圆Q的圆心轨迹为
,过l上一动点D作曲线
的两条切线,切点分别为A、B,直线
与y轴相交于点F,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42502a5730e1930d77d7100d1e34707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() ![]() | B.直线![]() |
C.![]() | D.以![]() ![]() |
您最近一年使用:0次
2022-11-28更新
|
831次组卷
|
4卷引用:高二数学第一学期期期末押题密卷03卷
解题方法
4 . 已知点F是抛物线
的焦点,动点P在抛物线上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/7e5a3835-f91e-40a8-aad4-47d71b82d280.png?resizew=238)
(1)写出抛物线的焦点坐标和准线方程;
(2)设点
,求
的最小值:
(3)设直线l与抛物线交于D,E两点,若抛物线上存在点P,使得四边形DPEF为平行四边形,证明:直线l过定点,并求出这个定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/7e5a3835-f91e-40a8-aad4-47d71b82d280.png?resizew=238)
(1)写出抛物线的焦点坐标和准线方程;
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46bcccb43d2bb69df350bc72cf8d6243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8769fe40da8b05f4fff38fa041cb60.png)
(3)设直线l与抛物线交于D,E两点,若抛物线上存在点P,使得四边形DPEF为平行四边形,证明:直线l过定点,并求出这个定点的坐标.
您最近一年使用:0次
名校
5 . 在平面直角坐标系中,抛物线
与
轴分别相交于
两点(点
在点
的左侧),与
轴相交于点
,设抛物线
的对称轴与
轴相交于点
,且
.
(1)求
的值;
(2)将抛物线
向上平移3个单位,得到抛物线
,设点
是抛物线
上在第一象限内不同的两点,射线
分别交直线
于点
,设
的横坐标分别为
,且
,求证:直线
经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850052d1b76efcb72b6dd236405b2158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07b3571ce1b8bb4e41285b668a279ce.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)将抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f5f4ad0caac5a0fecb64f3908d2290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ab53bfd448dd63a52a710900cf474e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd24f3c4bc9f9a75d4b28630bb630d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584aa3ab6160d92286cff2dc6a6c0ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584aa3ab6160d92286cff2dc6a6c0ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e81e3046baebc75ff78f7e2a76015b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42a0cb8e361b1e0bbccfdfa8950f0bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
解题方法
6 . 已知线段
是抛物线
的弦,且过抛物线焦点
.
(1)过点
作直线与抛物线对称轴平行,交抛物线的准线于点
,求证:
三点共线(
为坐标原点);
(2)设
是抛物线准线上一点,过
作抛物线的切线,切点为
.
求证:(i)两切线互相垂直;
(ii)直线
过定点,请求出该定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd2db5721001c9e91d46af36fbfbbb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3637509fd0c15e93a697a1ecd4d41a06.png)
求证:(i)两切线互相垂直;
(ii)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
您最近一年使用:0次
7 . 如图,过点
作抛物线
的两条切线
,
,切点分别是
,
,动点
为抛物线
上在
,
之间部分上的任意一点,抛物线
在点
处的切线分别交
,
于点
,
.
![](https://img.xkw.com/dksih/QBM/2022/5/18/2982217538543616/2983443164364800/STEM/a5fdc195-8935-4f5e-a9bf-d1bdb41c05b5.png?resizew=154)
(1)若
,证明:直线
经过点
;
(2)若分别记
,
的面积为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21872d8f6a518e0a2993ccf7a795ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/acc290b44635265137fdf13146b6a6d9.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/7f9e8449aad35c5d840a3395ea86df6d.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/2022/5/18/2982217538543616/2983443164364800/STEM/a5fdc195-8935-4f5e-a9bf-d1bdb41c05b5.png?resizew=154)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f92d681685fecaa72dcf38eda81852c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fee16a99d5b76a2bcaeb30d0c878d6f.png)
(2)若分别记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
2022·全国·模拟预测
8 . 已知
为坐标原点,抛物线
的方程为
,
的焦点为
,直线
与
交于
,
两点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2022-05-17更新
|
1669次组卷
|
9卷引用:2022年高考最后一卷(押题卷八)数学试题
(已下线)2022年高考最后一卷(押题卷八)数学试题(已下线)重难点14三种抛物线解题方法-1(已下线)山东省济南市2022届高三二模数学试题变式题11-16湖南省长沙市望城区第一中学2022-2023学年高二下学期期末模拟数学试题(已下线)第13讲 抛物线(9大考点)(2)河北省邯郸市魏县第五中学2022-2023学年高二上学期期末数学试题(已下线)第七节 抛物线 第二课时 直线与抛物线的位置关系 讲福建省厦门外国语学校2021-2022学年高二下学期数学期末模拟试题(2)(已下线)3.3.2 抛物线的几何性质(难点)-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)
解题方法
9 . 如图,已知点P在直线l:
上,A,B为抛物线C:
上任意两点,PA,PB均与抛物线C相切,直线AB与直线l交于点Q,过抛物线C的焦点F作AB的垂线交直线l于点K.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/22/e16b222d-fa45-4d97-8606-4ed702185d57.png?resizew=224)
(1)若点A到F的距离比到直线l的距离小1,求抛物线C的方程;
(2)在(1)的条件下,当
最小时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/22/e16b222d-fa45-4d97-8606-4ed702185d57.png?resizew=224)
(1)若点A到F的距离比到直线l的距离小1,求抛物线C的方程;
(2)在(1)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6d22a856a7378063b277eb9d33b2a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eedd1e9f48169405a92eef2668a878e.png)
您最近一年使用:0次
解题方法
10 . 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
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