名校
1 . 在平面直角坐标系
中,已知点
为抛物线
:
上一点,若抛物线
在点
处的切线恰好与圆
:
相切,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2d594684337ce067467e2a0ab1bb2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
2 . 已知抛物线C的顶点为原点,焦点F在x轴的正半轴,F到直线
的距离为
.点
为此抛物线上的一点,
.
(1)求抛物线方程和N点坐标;
(2)已知A、B是抛物线C上的两个动点,且点A在第一象限,点B在第四象限,直线
分别过点A、B且与抛物线C相切,P为
的交点.设C、D为直线
与直线
的交点,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23fc11a3a7592c68b20f93bdde2ed3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7116071164cdc45f5d312a437c68bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6c9ca0f54b6a84bb93d435933aae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715426331815c4e34ad97a8b66ab3ddd.png)
(1)求抛物线方程和N点坐标;
(2)已知A、B是抛物线C上的两个动点,且点A在第一象限,点B在第四象限,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
您最近一年使用:0次
名校
解题方法
3 . 已知F为抛物线C:
的焦点,点A在C上,
.点P(0,-2),M,N是抛物线上不同两点,直线PM和直线PN的斜率分别为
,
.
(1)求C的方程;
(2)存在点Q,当直线MN经过点Q时,
恒成立,请求出满足条件的所有点Q的坐标;
(3)对于(2)中的一个点Q,当直线MN经过点Q时,|MN|存在最小值,试求出这个最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0757f840f08c56d5d688cf4c1c25267b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(1)求C的方程;
(2)存在点Q,当直线MN经过点Q时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bee3672710a87854a3ecd3e169ffec.png)
(3)对于(2)中的一个点Q,当直线MN经过点Q时,|MN|存在最小值,试求出这个最小值.
您最近一年使用:0次
2024-05-11更新
|
1116次组卷
|
3卷引用:江苏省苏锡常镇四市2024届高三教学情况调研(二)数学试题
4 . 已知抛物线
,过点
的直线与抛物线交于
,
两点,则线段
中点
的轨迹方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
5 . 设抛物线
,直线
是抛物线C的准线,且与x轴交于点B,过点B的直线l与抛物线C交于不同的两点M,N,
是不在直线l上的一点,直线
,
分别与准线交于P,Q两点.
(1)求抛物线C的方程;
(2)证明:
:
(3)记
,
的面积分别为
,
,若
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad445f2f16d42d63980353981bdcf48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
(1)求抛物线C的方程;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2fd1dc3d012bef0ec559463298f5347.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61098066865164289ca1348b53420cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8503628bad86f077d1f6a4d801314f04.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/8060a00d925f27135a7baff2d0e9d598.png)
您最近一年使用:0次
2024-04-19更新
|
708次组卷
|
3卷引用:江苏省苏州市南京航空航天大学苏州附属中学2024届高三下学期五月阳光测试数学试题
名校
解题方法
6 . 应用抛物线和双曲线的光学性质,可以设计制造反射式天文望远镜,这种望远镜的特点是,镜铜可以很短而观察天体运动又很清楚.某天文仪器厂设计制造的一种反射式望远镜,其光学系统的原理如图(中心截口示意图)所示.其中,一个反射镜
弧所在的曲线为抛物线,另一个反射镜
弧所在的曲线为双曲线一个分支.已知
是双曲线的两个焦点,其中
同时又是抛物线的焦点,且,
的面积为10,
,则抛物线方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166614adaa6403cbd86ccf185e76fe8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3e7f96081bcc861028bd2f5a898663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc9dd082b268de562c6534296a7f84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed9d829d7179e8ff05814c93e047eb5.png)
您最近一年使用:0次
2024-03-31更新
|
1697次组卷
|
3卷引用:江苏省无锡市锡东高级中学2024届高三下学期4月月考数学试题
2024高三下·江苏·专题练习
解题方法
7 . 已知抛物线
:
过点
,
,
是抛物线
上的两个动点,直线
的斜率与直线
的斜率之和为4,则直线
恒过定点__________ .
![](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/86a6be776cdd229e5c1339265b23624a.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
8 . 在平面直角坐标系
中,点
,点A为动点,以线段
为直径的圆与
轴相切,记A的轨迹为
,直线
交
于另一点B.
(1)求
的方程;
(2)
的外接圆交
于点
(不与O,A,B重合),依次连接O,A,C,B构成凸四边形
,记其面积为
.证明:
的重心在定直线上;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f449cadb49859b80c31ef1f68bfe81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea16ceca816f7d3d50650af141baf42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
9 . 已知抛物线
的焦点为F,A为抛物线上一点,延长
交抛物线于点B,抛物线的准线与x轴的交点为K,
,
.
(1)求抛物线的方程;
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719d4da5a19c051c4b344500dd67cff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b059953265c17fd38adcb5ff24de4a.png)
(1)求抛物线的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1028cdd34b2ec5e663dd1f8092a32a3e.png)
您最近一年使用:0次
10 . 已知抛物线
:
(
)的焦点为
,过拋物线
上一点
作两条斜率之和为0的直线,与
的另外两个交点分别为
,
,则下列说法正确的是( )
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f54dd475ff1321041c80738b201c3b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.![]() ![]() |
B.直线![]() ![]() |
C.若圆![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次