已知两点M(-2,0)、N(2,0),点P为坐标平面内的动点,满足|MN|•|MP|+MN•NP=0,则动点P(x,y)的轨迹方程为( ) A.y2=8x B.y2=-8x C.y2=4x D.y2=-4x
问题描述:
已知两点M(-2,0)、N(2,0),点P为坐标平面内的动点,满足|
|•|MN
|+MP
•MN
=0,则动点P(x,y)的轨迹方程为( )NP
A. y2=8x
B. y2=-8x
C. y2=4x
D. y2=-4x
答
设P(x,y),x>0,y>0,M(-2,0),N(2,0),|
|=4MN
则
=(x+2,y),MP
=(x−2,y)NP
由|
|•|MN
|+MP
•MN
=0,NP
则4
+4(x−2)=0,
(x+2)2+y2
化简整理得y2=-8x.
故选B