Question

一动点到定点A(12,16)的距离等于它到定点B(3,4)的距离的2倍,求动点的轨迹方程 求详解

Answer 1

设点P坐标是(x,y)

PA=2PB

PA^2=4PB^2

即有:(x-12)^2+(y-16)^2=4[(x-3)^2+(y-4)^2]

x^2-24x+144+y^2-32y+256=4x^2-24x+36+4y^2-32y+64

即有:3x^2+3y^2=300

即轨迹方程是一个圆:x^2+y^2=100