已知点M(3,2)N(1/2) 点P在抛物线Y^2X上,且|PM|+|PN|取最小值,则P的坐标为

纠正题意：已知点M(3,2)N(1,2) 点P在抛物线Y^2=X上,且|PM|+|PN|取最小值,则P的坐标为?解:设P(yo^2,yo)(yo∈N※) ∵向量PM+向量PN>向量MN 向量MN=2 ∴向量PM+向量PN>2 又∵向量PM+向量PN=根号[(yo^2-1)^2+(yo-2)^2]+根号[(yo^2-3)^2+(yo-2)^2]>2最后算得(yo-根号37-1）（yo+根号37+1)>0∴yo>(根号37-1)/6或yo