Question

已知椭圆的焦点为F1(-√3,0)m右顶点为P(2,0)设点A（1,0.5) 若P是椭圆上的动点,求线段PA中点M的轨迹

Answer 1

椭圆中：c=√3,a=2

==>b=1

设P(2cosα,sinα)……………………椭圆参数方程

M(cosα+0.5,0.5sinα+0.25)

==>即:x=cosα+0.5,y=0.5sinα+0.25

==>cosα=x-0.5,sinα=2y-0.5

==>(cosα)^2+(sinα)^2=(x-0.5)^2+(2y-0.5)^2=1

即：M的轨迹方程是 (x-0.5)^2+(2y-0.5)^2=1