名校
解题方法
1 . 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
2 . 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:四川省成都市成华区嘉祥外国语高级中学高2023-2024学年高二下学期3月月考数学试题
3 . 已知抛物线
的焦点为
,过点
倾斜角为
的直线
交抛物线与
两点.点
在
轴上方,点
在
轴下方.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/8c2b10f3-0cf6-43bc-9988-81e797d2c5af.png?resizew=159)
(1)求证:
;
(2)若
,试求
的取值范围;
(3)如图,过焦点
作互相垂直的弦
,若
与
的面积之和最小值为32,求抛物线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa877db8dc1b03f1581106dfd5211ac4.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/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/8c2b10f3-0cf6-43bc-9988-81e797d2c5af.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d272d156ab8110bdd21ead74aad0ee6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ce877f1c5f2ffb17e10bec7e5869cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ca17c81683a8bf4f8c143d41de298ea.png)
(3)如图,过焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947a9e717f8bd9e2f5eb3ba8929932a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fb6e81fee5674c3e26a65e58cc506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e64c953aaf341e772a5fe776fbc78a.png)
您最近一年使用:0次
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: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
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)(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)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)
5 . 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
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4卷引用:福建省泉州市实验中学2023-2024学年高二上学期1月考试数学试题