1 . 在平面直角坐标系
中,一动圆经过点
且与直线
相切,设该动圆圆心的轨迹为曲线K, P是曲线K上一点.
(1)当
时,求曲线K的轨迹方程;
(2)已知过点A 且斜率为k的直线l与曲线K交于B,C 两点,若
且直线
与直线
交于Q点.求证:
为定值:
(3)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
且点 D,E在y轴上,
的内切圆的方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6316e0e6da742e9b035d8f2cc91a4dd.png)
求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46110ded9a784e1e68684714746c9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853e3c15d116fb61f236ab239c50b114.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)已知过点A 且斜率为k的直线l与曲线K交于B,C 两点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96968cc368104c626e7cdf658e361c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a249bee4ac9de17327ca5399e5077ca5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6316e0e6da742e9b035d8f2cc91a4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
您最近一年使用:0次
2 . 设抛物线
的焦点为
,过
且斜率为1的直线与
交于
两点,且
.
(1)求抛物线
的方程;
(2)已知过点
的直线
与
交于不重合的两点
,且
,直线
和
的斜率分别为
和
.求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c42d88e496a17562d25195301e0ac2.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ed9d97b8745ed1c15349ea3fffc299.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530e5817131adf2c05b99ff18eb9060f.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/1456e81321ccb20077b34562ca9cffbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090b7ee52d644d0c630ef44aec1726dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63e9a213f3dd57269cf4ff02d6212e0.png)
您最近一年使用:0次
2024-01-03更新
|
673次组卷
|
4卷引用:微考点6-6 圆锥曲线中斜率和积与韦达定理的应用
3 . 设抛物线
,过焦点
的直线与抛物线
交于点
、
.当直线
垂直于
轴时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/4aa9e607-413f-4aea-bdbc-427ada0cd9a0.png?resizew=164)
(1)求抛物线
的标准方程.
(2)已知点
,直线
、
分别与抛物线
交于点
、
.
①求证:直线
过定点;
②求
与
面积之和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544fc1ddf9f59d08c9feb5df9b4080d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c663466d641b5fdfef1e529d6c330ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166afeb61d5a80366a8ae29c912cd644.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/08e39fda3cda5ddc03b085413f2030aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/4aa9e607-413f-4aea-bdbc-427ada0cd9a0.png?resizew=164)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96499747e4aea990f4b878eea8d73ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.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/8455657dde27aabe6adb7b188e031c11.png)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
您最近一年使用:0次
2024-02-28更新
|
1068次组卷
|
4卷引用:专题3 焦点弦题 性质优先 【练】
名校
解题方法
4 . 设抛物线
,过焦点
的直线与抛物线
交于点
、
.当直线
垂直于
轴时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/24/11804ba6-02c8-411e-94fb-ae09a83adffc.png?resizew=145)
(1)求抛物线
的标准方程.
(2)已知点
,直线
、
分别与抛物线
交于点
、
.求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.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/ae5a64bcb77f5f64e4af6930c249a270.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/24/11804ba6-02c8-411e-94fb-ae09a83adffc.png?resizew=145)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2024-01-09更新
|
998次组卷
|
5卷引用:模块七 圆锥曲线(测试)
(已下线)模块七 圆锥曲线(测试)(已下线)专题18 圆锥曲线高频压轴解答题(16大题型)(练习)安徽省合肥市第一中学2023-2024学年高二上学期1月考数学考试试题宁夏回族自治区银川市贺兰县第一中学2023-2024学年高二上学期期末复习数学试题(二)广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(三)
名校
解题方法
5 . 已知抛物线
与椭圆
有公共的焦点.
的标准方程.
(2)如图,过抛物线
的焦点
的直线与抛物线
交于点
,点
,直线AP,BP分别与抛物线
交于点
.证明:
①直线CD过定点;
②
与
的面积之比为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50996be3c0d950d6ef58110948b7fbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82766cfd2b7c59c7fac5b827ae5863b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)如图,过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de77ee0b176035fd3a89edc2ad957a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
①直线CD过定点;
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
您最近一年使用:0次
23-24高二上·全国·课后作业
解题方法
6 . 如图,
是抛物线
对称轴上一点,过点M作抛物线的弦AB,交抛物线于A,B.
,求弦AB中点的轨迹方程;
(2)过点M作抛物线的另一条弦CD,若AD与y轴交于点E,连接ME,BC,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbfc5253a678d786c9a8091fff43729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
(2)过点M作抛物线的另一条弦CD,若AD与y轴交于点E,连接ME,BC,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/490111e9e5aefb170410f0501134d22e.png)
您最近一年使用:0次
7 . 直线
过抛物线
的焦点
,且与抛物线交于
,
不同的两点,点
在抛物线的准线上,且
//
轴.
(1)证明:
;
(2)判断直线
是否经过坐标原点,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af529571cca0e6957a197fe3f878d419.png)
(2)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
真题
名校
8 . 如图,在平面直角坐标系xOy中,已知直线l:x
y
2=0,抛物线C:y2=2px(p>0).
(2)已知抛物线C上存在关于直线l对称的相异两点P和Q.
①求证:线段PQ的中点坐标为
;
②求p的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc339cf6dd66599db64fa3fa44e608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc339cf6dd66599db64fa3fa44e608.png)
(2)已知抛物线C上存在关于直线l对称的相异两点P和Q.
①求证:线段PQ的中点坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594db0025f37b18ab6f2b2d1b5f6b1b2.png)
②求p的取值范围.
您最近一年使用:0次
2016-12-04更新
|
3855次组卷
|
15卷引用:专题24 解析几何解答题(文科)-3
(已下线)专题24 解析几何解答题(文科)-3(已下线)专题24 解析几何解答题(理科)-2(已下线)专题9.8 直线与圆锥曲线位置关系(练)-江苏版《2020年高考一轮复习讲练测》(已下线)专题9.7 抛物线(练)-江苏版《2020年高考一轮复习讲练测》(已下线)专题18 解析几何综合-五年(2016-2020)高考数学(文)真题分项(已下线)专题18 解析几何综合-五年(2016-2020)高考数学(理)真题分项(已下线)对点练60 抛物线的性质-2020-2021年新高考高中数学一轮复习对点练(已下线)专题13 解析几何中的范围、最值和探索性问题 第一篇 热点、难点突破篇(讲)-2021年高考数学二轮复习讲练测(浙江专用)2016年全国普通高等学校招生统一考试数学(江苏卷精编版)(已下线)章末质量检测3 圆锥曲线与方程-2018年数学同步优化指导(北师大版选修2-1)河北省张家口第一中学2019-2020学年高二(衔接班)9月月考数学试题北京市北京一零一中学2019-2020学年高二第一学期期末考试数学试题北京市101中学2019-2020学年上学期高二年级期末考试数学试题湖北省宜昌市英杰学校2021-2022学年高二上学期12月月月考数学试题(已下线)2016年全国普通高等学校招生统一考试数学(江苏卷参考版)