名校
解题方法
1 . 已知抛物线
,定点
.
(1)过点
且过抛物线
的焦点
的直线,交抛物线
于
、
两点,求
;
(2)求过点
且与抛物线
有且仅有一个公共点的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/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/3f4dfec890cdfdda355e19463f3be813.png)
(2)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2 . 过抛物线
的焦点且斜率为1的直线交抛物线于A、B两点,已知
.
(1)求抛物线的方程;
(2)O为坐标原点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82796f5bb05438453a1e06a4fa83d6a1.png)
(1)求抛物线的方程;
(2)O为坐标原点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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名校
3 . (1)求圆
和圆
的公切线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
与抛物线
相交,求弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5b68c97448290f6ed3172bdf384abf.png)
![](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/732cec7b8b8554dba130da909c6ec8bf.png)
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名校
4 . 已知直线
过抛物线
的焦点
,与
相交于
两点,且
.若线段
的中点的横坐标为3,直线
的斜率为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48867e261c61d24a0a1a4f7ff4627c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
5 . 已知抛物线
的焦点为F,点
,N是抛物线C上一点,当
取得最小值时,
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64447af8454c613a58b11d9274d3da2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356547c08d2cd7ba5a6aaf412266d7b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1622b71bf051bfd14c79b2c75eca58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33181b27b10690b4913595f8c1f46e.png)
A.![]() | B.5 | C.![]() | D.12 |
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名校
解题方法
6 . 设抛物线
的焦点为F,过F且斜率为2的直线l与C交于P、Q两点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c84a09595eabd6ae21a2e8faa7465c.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c84a09595eabd6ae21a2e8faa7465c.png)
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2024-04-10更新
|
454次组卷
|
3卷引用:四川省德阳市第五中学2023-2024学年高二下学期4月月考数学试题
7 . 已知抛物线C:
的焦点与双曲线E:
的右焦点重合,双曲线E的渐近线方程为
.
(1)求抛物线C的标准方程和双曲线E的标准方程.
(2)斜率为1且纵截距为
的直线l与抛物线C交于A、B两点,O为坐标原点,求
的面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6d8eaacc2d999b37209feba103f9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0e308d06579ae683524a6c04d9872c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1958855dabc2b117503c0ebbe1eee7e7.png)
(1)求抛物线C的标准方程和双曲线E的标准方程.
(2)斜率为1且纵截距为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74eb8a7738402df52d4a97262b85ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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8 . 在平面直角坐标系xOy中,已知抛物线的焦点为F,过点F且倾斜角为120°的直线
与抛物线C交于A,B两点,其中点A在第一象限,若
,则
的面积为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-03-26更新
|
273次组卷
|
2卷引用:湖北省恩施州咸丰春晖高级中学2023-2024学年高二下学期第一次月考数学试题
解题方法
9 . 已知抛物线
,过点
作一条直线l与抛物线交于
两点,恰使得点
平分
,则直线
的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c11f3ce51cd741781cf2ffeb6e8b80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02eb5ecd23cde2fd451714281f0657af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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10 . 已知:抛物线的顶点在原点,焦点在
轴的正半轴上,直线
与抛物线相交于两点
,且
,求抛物线
的方程.
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