2024·全国·模拟预测
名校
解题方法
1 . 在平面直角坐标系
中,已知
是
轴上的动点,
是平面内的动点,线段
的垂直平分线交
轴于点
,交
于点
,且
恰好在
轴上,记动点
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,直线
与直线
分别交于点
,设线段
的中点为
,求证:点
在曲线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ebc04d37e416fbb039642fd127a7d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ebc04d37e416fbb039642fd127a7d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.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/42a2b8b43e1fe82fc439d145e91b860c.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139c0ae68e597571ba72ef727fa9222c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
名校
解题方法
2 . 已知抛物线
,O是坐标原点,过
的直线与E相交于A,B两点,满足
.
(1)求抛物线E的方程;
(2)若
在抛物线E上,过
的直线交抛物线E于M,N两点,直线
,
的斜率都存在,分别记为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c42d88e496a17562d25195301e0ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(1)求抛物线E的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18c261201283d56c071c1c8133dc20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b72de4221a7de45fad497d0bb7ac1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.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/6b881044b5c73db6fcce110525741b02.png)
您最近一年使用:0次
2024-04-10更新
|
1050次组卷
|
3卷引用:宁夏回族自治区石嘴山市平罗中学2024届高三下学期第三次模拟考试数学(理)试题
3 . 已知抛物线,过抛物线的焦点F且斜率为
的直线l与抛物线相交于不同的两点A,B,
.
(1)求抛物线C的方程;
(2)点M在抛物线的准线上运动,过点M作抛物线C的两条切线,切点分别为P,Q,在平面内是否存在定点N,使得直线MN与直线PQ垂直?若存在,求出点N的坐标;若不存在,请说明理由.
您最近一年使用:0次
2023-04-16更新
|
596次组卷
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5卷引用:宁夏回族自治区石嘴山市大武口区石嘴山市第三中学2023届高三三模理科数学试题
宁夏回族自治区石嘴山市大武口区石嘴山市第三中学2023届高三三模理科数学试题河南省平顶山市等2地普高联考2022-2023学年高三下学期测评(五)理科数学试题(已下线)重难点突破12 双切线问题的探究(六大题型)(原卷版)-1(已下线)高二上学期期中复习【第三章 圆锥曲线的方程】十二大题型归纳(拔尖篇)-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)通关练17 抛物线8考点精练(3)
名校
解题方法
4 . 已知抛物线
:
经过点
,焦点为F,PF=2,过点
的直线
与抛物线
有两个不同的交点
,
,且直线
交
轴于
,直线
交
轴于
.
(1)求抛物线C的方程
(2)求直线
的斜率的取值范围;
(3)设
为原点,
,
,求证:
为定值.
![](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/d3e91ec3c93c6cd6affce79b2e270a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1200a60bad1f19b75bc4b85ca45c43.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求抛物线C的方程
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf235268ea182e3785101b44e74df3e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762af77333604db19016178d2217adb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587b693b82241eb9c32cdbb96c209f33.png)
您最近一年使用:0次
2022-05-11更新
|
1913次组卷
|
5卷引用:宁夏石嘴山市第一中学2022届高三下学期第三次模拟数学(理)考试题
宁夏石嘴山市第一中学2022届高三下学期第三次模拟数学(理)考试题浙江省2022届高三下学期高考冲刺卷(二)数学试题(已下线)专题12 定比点差法及其应用 微点5 定比点差法综合训练(已下线)9.5 三定问题及最值(精练)(已下线)专题13 平面向量(模拟练)-2
名校
解题方法
5 . 在平面直角坐标系
中,动点
到点
的距离比到直线
的距离小2.
(1)求
的轨迹的方程;
(2)设动点
的轨迹为曲线
,过点
作斜率为
,
的两条直线分别交
于M,N两点和P,Q两点,其中
.设线段
和
的中点分别为A,B,过点
作
,垂足为
.试问:是否存在定点
,使得线段
的长度为定值.若存在,求出点
的坐标及定值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14436636ec6a7aec09cb63cecf6e970d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7e51699bcf9d57cc560edded62d3ec.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)设动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec7bcf5820dfe70290259c2d7ac1ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33daacca5f6f6681b662295ebb98587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1ab6c10bc0a8bfbdc3b4824c2de1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2022-04-20更新
|
1708次组卷
|
7卷引用:宁夏石嘴山市第三中学2022届高三第三次模拟考试数学(理)试题
宁夏石嘴山市第三中学2022届高三第三次模拟考试数学(理)试题山东省枣庄市2022届高三下学期一模数学试题(已下线)秘籍10 抛物线-备战2022年高考数学抢分秘籍(全国通用)(已下线)2022年高考考前20天终极冲刺攻略(三)【数学】(新高考地区专用)(5月29日)四川省绵阳市南山中学实验学校2024届高三(补习班)上学期11月月考数学(理)试题(已下线)专题3.16 圆锥曲线中的定点、定值、定直线问题大题专项训练(30道)-2022-2023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)四川省资阳中学2022-2023学年高二下学期三月月考数学(文科)试题
6 . 过抛物线
的焦点F作不平行于x轴的直线交抛物线于A,B两点,过A,B分别作抛物线的切线相交于C点,直线
交抛物线于D,E两点.
(1)求
的值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b183c3397b34f1b1258a3e25eec4a22.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70cb494c1b7687b984afc1fd8d9f5b43.png)
您最近一年使用:0次
2021-05-16更新
|
431次组卷
|
3卷引用:宁夏石嘴山市2021届高三下学期三模数学(理)试题
名校
7 . 已知抛物线
的焦点为F,准线与x轴交点为T,点G在E上且
轴,
的面积为
.
(1)求E的方程;
(2)已知点
,
,
,点A是E上任意一点(异于顶点),连接
并延长交E于另一点B,连接
并延长交E于另一点C,连接
并延长交E于另一点D,当直线
的斜率存在时,证明:直线
与
的斜率之比为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4c5119c63ea86e97ad2ac7c84a423b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8afbdf92080953b4093dc30e37aded91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
(1)求E的方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8293156150e4eb50a1bdd71090917dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6129110e508ca0fa4aec666d2684ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33e1e069c283602b5a7844d25b81e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb6fd2fa53b92a03d21f208b74e3857.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/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2021-05-13更新
|
495次组卷
|
3卷引用:宁夏石嘴山市平罗中学2022届高三第四次模拟考试数学(理)试题
宁夏石嘴山市平罗中学2022届高三第四次模拟考试数学(理)试题云南省昆明市2021届高三三模数学(文)试题(已下线)第3讲 圆锥曲线中的证明、定值、定点问题(练)-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)
名校
8 . 在直角坐标系
中,直线
与抛物线
交于
,
两点,且
.
(1)求
的方程;
(2)试问:在
轴的正半轴上是否存在一点
,使得
的外心在
上?若存在,求
的坐标;若不存在,请说明理由..
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fceb9eb57ca36db386ffafeda213599c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.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/3825ccc273ef9a672a606432d165b866.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)试问:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e1441a49e782ff0ef46e776cde06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2018-12-29更新
|
841次组卷
|
6卷引用:【全国百强校】宁夏石嘴山市第三中学2019届高三下学期三模考试数学(理)试题
【全国百强校】宁夏石嘴山市第三中学2019届高三下学期三模考试数学(理)试题【校级联考】河北省省级示范高中联合体2019届高三12月联考数学(文)试题【市级联考】河北省邢台市2019届高三期末测试数学(文)试题陕西省榆林市第一中学2019届高考模拟考试文科数学 试题陕西省榆林市一中2019届高考模拟考试理科数学 (已下线)专题9.8 圆锥曲线的综合问题(精练)-2021年高考数学(文)一轮复习讲练测
名校
9 . 已知抛物线
经过点
,
在点
处的切线交
轴于点
,直线
经过点
且垂直于
轴.
(1)求线段
的长;
(2)设不经过点
和
的动直线
交
于点
和
,交
于点
,若直线
、
、
的斜率依次成等差数列,试问:
是否过定点?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c6e4418e49a475db5b4a95bc33b3836.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
(2)设不经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f51186dfbcc1210feb65603134a2588.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
您最近一年使用:0次
2016-12-04更新
|
408次组卷
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6卷引用:2016届宁夏石嘴山三中高三下四模理科数学试卷