Question

做圆P过B(2,0)且与圆(x+2)2+y2=1外切 则动圆圆心P的轨迹方程为

Answer 1

P(x,y)

动圆P过B(2,0)

(x-2)^2+y^2=r^2.(1)

与圆A:(x+2)2+y2=1外切,A(-2,0),rA=1

PA^2=(x+2)^2+y^2=(r+1)^2.(2)

(2)-(1):

8x=1+2r

r=(8x-1)/2

(x-2)^2+y^2=r^2=[(8x-1)/2]^2

60x^2-4y^2=15

动圆圆心P的轨迹方程为双曲线:

x^2/0.25-y^2/3.75=1