设点P坐标为(x,y).则由条件得
√[(x-1)²+y²]=√2/2*|(x-2)|
(x-1)²+y²=(x-2)²/2
2(x-1)²+2y²=(x-2)²
2x²+2-4x+2y²=x²+4-4x
x²-2+2y²=0
整理得x²/2+y²=1
所以动点P的轨迹为椭圆.