题目
题型:不详难度:来源:
(1)求证:FM1⊥FN1;
(2)记△FMM1、△FM1N1、△FNN1的面积分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132500-49520.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132500-85346.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132500-12109.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-54677.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132500-49520.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132500-12109.gif)
答案
(1)略
(2)略
解析
∴∠MFM1=∠MM1F,∠NFN1=∠NN1F.
如图,设准线l与x轴的交点为F1.
∵MM1∥NN1∥FF1,
∴∠F1FM1=∠MM1F,∠F1FN1=∠NN1F.
而∠F1FM1+∠MFM1+∠F1FN1+∠NFN1=180o,
即2∠F1FM1+2∠F1FN1=180o,
∴∠F1FM1+∠F1FN1=90o,
即∠M1FN1=90o,故FM1⊥FN1.
证法二:依题意,焦点为F(
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
设点M,N的坐标分别为M(x1,y1),N(x2,y2),直线MN的方程为x=my+
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-99797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-55452.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-12835.gif)
于是,y1+y2=2mp,y1y2=-p2.
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-99797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-55452.gif)
(2)S
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-54677.gif)
证法一:设M(x1,y1),N(x2,y2),
直线l与x轴的交点为F1,则由抛物线的定义得
|MM1|=|MF|=x1+
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
S1=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-11560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-11560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
S2=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-11560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-11560.gif)
S3=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-11560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-11560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
∵S
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-54677.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-27280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-11560.gif)
=4×
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-11560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-11560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-27280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132502-92801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-57579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132503-37649.gif)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132503-54186.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132504-42884.gif)
p2(m2p2+p2)=p2(m2p2+p2),此式恒成立. 故S
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132501-54677.gif)
核心考点
试题【(12分)过抛物线y2=2px(p>0)的焦点F的直线与抛物线相交于M、N两点,自M、N向准线l作垂线,垂足分别为M1、N1.(1)求证:FM1⊥FN1;(2)】;主要考察你对抛物线的定义与方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132436-86257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132436-82581.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132432-12122.png)
A.(0,![]() | B.(![]() | C.(1,0) | D.(0,1) |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132407-30028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132408-76608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132408-82649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132402-14760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132402-96640.png)
A.18 | B.24 | C. 36 | D. 48 |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132351-97828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132351-61932.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025132351-57319.gif)
最新试题
- 1仿生学是一门蓬勃发展的学科,该学科主要是 [ ]A.将动物基因进行改造,使动物生产出人类所需要的物质B.将动物
- 2下列关于隐性性状的叙述不正确的是 [ ]A.生物体不能表现出来的性状B.由隐性基因决定的性状C.具有相对性状的纯
- 3公司是市场经济在数百年孕育和发展过程中,逐步形成的企业的一种重要形式。我国的法定公司形式有股份有限公司和有限责任公司。两
- 4如果,那么= ▲ .
- 5柿子熟了从树上自然掉落下来,下面哪一幅图可以大致刻画出柿子下落过程中(即落地前)的速度变化情况[ ]A.B.C.
- 6板块构造学说认为[ ]A.地球的岩石图由五大板块拼合而成B.板块交界地带是世界主要火山、地震分布带C.板块内部稳
- 7I stay at home _______ on weekends, but I don’t feel ______.
- 8根据以下规定的情境,以“免疫力”为中心,分别扩展成一段话,每段40字左右。情境一:身体健康方面_____________
- 9设λ为实数,a,b,c为向量,则下列命题中的假命题是( )A.a+b=b+aB.a•b=b•aC.λ(a+b)=λa+
- 10 亲爱的同学,你的书架上或同学的课桌里可能有这些书籍:史铁生的《秋天的怀念》、白岩松的《痛并快乐着》、郭敬明
热门考点
- 1. ‘ Time ____ will never be found again!’ I couldn’t help ta
- 2A new cinema _ in our city last year.A.built B.was built C.w
- 3设,则的最小值是 .
- 4某年12月,***在一次党内外人士座谈会上指出,政协仍有存在的必要,但是我们不能把政协搞成国家权力机关。此话的主要背景是
- 5沿海航线中,北方沿海航线和南方沿海航线的分界线是( )A.天津B.湛江C.北海D.厦门
- 6(11分)Ⅰ.(1)0.02 mol·L-1的HCN溶液与0.02 mol·L-1 NaCN溶液等体积混合,已知该混合溶
- 7在△ABC中,∠C=90°,sinB=12,则tanA的值为( )A.3B.1C.33D.12
- 8根据句意及首字母提示完成下列句子。1. He comes from France. He speak F_____. 2
- 9 写一则消息,报道本校或本班新近开展的一项有意义的活动。要求真实准确,迅速及时,简洁明快,用事实说话。
- 10下图是动物细胞有丝分裂某一时期图像,请据图回答问题。(1)该细胞处于分裂期的_________期,细胞中有_______