1 . 已知抛物线
.
(1)直线
与
交于
、
两点,
为坐标原点.
从下面的①②两个问题中任选一个作答,如果两个都作答,则按所做的第一个计分.
①证明:
.
②若
,求
的值;
(2)已知点
,直线
与
交于
、
两点(均异于点
),且
.过
作直线
的垂线,垂足为
,试问是否存在定点
,使得
为定值?若存在,求出定值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf6b28846321fab48ffd3543af62e3d2.png)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764ab1262baa09cd62fb6ddba39df2ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.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/1dde8112e8eb968fd042418dd632759e.png)
从下面的①②两个问题中任选一个作答,如果两个都作答,则按所做的第一个计分.
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a3665f46dacc3b807cc814467b0622.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49a4c11d41372175ba3541a44c3376b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b986e3613290b456532843d5ad4c6e67.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530e5817131adf2c05b99ff18eb9060f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321497d8f04117d3c44986d6b1ff606a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/c71684a46ec1ba25ba0b5a530995310f.png)
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2 . 已知直线
经过抛物线
的焦点
,且与
交于
,
两点,过
,
分别作直线
的垂线,垂足依次记为
,若
的最小值为
,则()
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.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/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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b64b91d079810d968b9ef63e3284c7af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
A.![]() |
B.![]() |
C.![]() |
D.若点![]() ![]() ![]() ![]() ![]() ![]() |
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4卷引用:河北省石家庄市第二中学2024届高三上学期第一次模拟测试数学试题
3 . 已知直线
的方向向量与直线
的方向向量共线且过点
;
(1)求
的方程;
(2)若
与抛物线
交于点
为坐标原点,设直线
,直线
的斜率分别是
;求
及
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089243ad31b799d65b9e86ec2a116188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f739a29d4fbb88ba1337e8456ef1f8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876856cdb3900b117f280615c185d347.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/4ad608ff2250d3f93f509ef52fff7611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb8956ebcde7cf0f1011a2fc1888e15.png)
您最近一年使用:0次
2023-11-19更新
|
730次组卷
|
3卷引用:河北省石家庄市第二十七中学2023-2024学年高二上学期第三次月考数学试题
解题方法
4 . 已知
为抛物线
上不同两点,
为坐标原点,
,过
作
于
,且点
.
(1)求直线
的方程及抛物线
的方程;
(2)若直线
与直线
关于原点对称,
为抛物线
上一动点,求
到直线
的距离最短时,
点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00148717f95c6427487c1e55baa1844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4d4326764365ee287cd6974853668b.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
5 . 已知抛物线
的焦点为F,过点F作互相垂直的两条直线与抛物线E分别交于点A,B,C,D,P,Q分别为
,
的中点,O为坐标原点,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4fb72e39d79b7a0cd892fa5fa34bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
A.![]() |
B.![]() |
C.若F恰好为![]() ![]() ![]() |
D.直线![]() ![]() |
您最近一年使用:0次
2024-01-14更新
|
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4卷引用:河北省衡水市冀州中学2024届高三第一次调研数学试题
名校
解题方法
6 . 已知直线
过抛物线
的焦点F,且与抛物线C交于A,B两点,过A,B两点分别作抛物线准线的垂线,垂足分别为M,N,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a530718ec0d7a7ce306a9144fe409a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
A.抛物线的方程为![]() | B.线段![]() ![]() |
C.线段![]() ![]() | D.![]() |
您最近一年使用:0次
2023-02-22更新
|
714次组卷
|
4卷引用:河北省石家庄市2022-2023学年高二上学期期末数学试题
河北省石家庄市2022-2023学年高二上学期期末数学试题河北省石家庄市二十三中2022-2023学年高二上学期期末数学试题(已下线)安徽省(九师联盟)2023届二模数学试题变式题11-16(已下线)模块四 专题4 暑期结束综合检测4(能力卷)(人教B)
7 . 已知抛物线C:
的焦点F到准线l的距离为2,圆
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c6c1a4e1df4d42eddb81d25e8c4775.png)
(1)若第一象限的点P,Q是抛物线C与圆的交点,求证:点F到直线PQ的距离大于1;
(2)已知直线l:
与抛物线交于M,N两点,
,若点N,G关于x轴对称,且M,A,G三点始终共线,求t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3557809c066e68395b614535a7675e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c6c1a4e1df4d42eddb81d25e8c4775.png)
(1)若第一象限的点P,Q是抛物线C与圆的交点,求证:点F到直线PQ的距离大于1;
(2)已知直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46de5f5993e7dcd0e828081045e502af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236cfb6e8e16ce032b50d3c9539fb05a.png)
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2023-04-09更新
|
710次组卷
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4卷引用:河北省唐山市开滦第二中学2023届高三一模数学试题
河北省唐山市开滦第二中学2023届高三一模数学试题(已下线)模块六 专题1 易错题目重组卷(河北卷)江西省抚州市乐安县2022-2023学年高二下学期期中考试数学试题江西省抚州市乐安县第二中学2022-2023学年高二下学期期中数学试题
解题方法
8 . 已知抛物线
:
(
),过点
的直线
与抛物线
交于
,
两点(
在
的左侧),
为线段
的中点.当直线
斜率为
时,中点
的纵坐标为
.
(1)求抛物线
的方程;
(2)若线段
上存在点
,使得
,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fe4f072728afb26b643dbe9e2e0f48.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/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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c68ac2cde21d05eeaa247847e9c73e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
名校
解题方法
9 . 已知抛物线
的焦点为F,且A,B,C三个不同的点均在
上.
(1)若直线AB的方程为
,且点F为
的重心,求p的值;
(2)设
,直线AB经过点
,直线BC的斜率为1,动点D在直线AC上,且
,求点D的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a9efe4c27ce894634c9e4c737b5fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(1)若直线AB的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ba50e25f0d2099dce13f113685d233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cda12642d59a5817e8990c43de20535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7711afeb265550ead8321ea2a24d5.png)
您最近一年使用:0次
2024-01-18更新
|
608次组卷
|
4卷引用:河北省邢台市部分重点高中2023-2024学年高二上学期1月期末数学试题
名校
解题方法
10 . 已知抛物线
经过点
.
(1)求抛物线
的标准方程及其准线方程;
(2)过点
的直线交抛物线
于A、
两点,
为坐标原点,记直线
,
的斜率分别为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3aad8bd7a7f5a1bff9ee176efbcadd9.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a0d4c22734cac795de1e5c5fbefa87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
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2023-10-30更新
|
604次组卷
|
2卷引用:河北省衡水市第二中学2023-2024学年高二上学期四调数学试题