已知抛物线 $y^2=2px\left(p>0\right)$的焦点为 $F$，点 $P_1\left(x_1,y_1\right)$、 $P_2\left(x_2,y_2\right)$、 $P_3\left(x_3,y_3\right)$在抛物线上，且 $2x_2=x_1+x_3$，则有（）

A．	$\left|F{P}_1\right|-\left|F{P}_2\right|=\left|F{P}_3\right|$	B．	${\left|F{P}_1\right|}^2-{\left|F{P}_2\right|}^2={\left|F{P}_3\right|}^2$
C．	$2\left|F{P}_2\right|=\left|F{P}_3\right|+\left|F{P}_1\right|$	D．	${\left|F{P}_2\right|}^2=\left|F{P}_1\right|·\left|F{P}_3\right|$