长度为3的线段AB的两个端点A,B分别在x,y轴上移动,点P在直线AB上且满足BP=2PA(1)求点P的轨迹方程;(

2025-12-05 09:20:45
推荐回答(1个)
回答1:

(1)设A(m,0),B(0,n),P(x,y)

BP
=2
PA
,得x=2(m-x),y-n=2(0-y),
即m=
3
2
x,n=3y,
又由|AB|=
m2+n2
=3得:
x2
4
+y2=1
,即为点P的轨迹方程.
(2)设直线?的方程为y=x+b,E(x1,y1),F(x2,y2),
y=x+b
x2
4
+y2=1
得:
5
4
y2?
b
2
y+
b2?4
4
=0

则y1+y2=
2b
5
,y1y2=
b2?4
5

则△QEF面积S=
1
2
(y1+y2)|y1-y2|=