Tangents are drawn from (−2,0) to y2=8x, radius of circle(s) that would touch these tangents  and the corresponding chord of contact, can be equal to,

Point ' P ' clearly lies on the directrix of y2=8x.  Thus slope of PA and PB are 1 and −1 respectively.  Equation of PA:y=x+2, equation of PB:y=−x−2, equation of AB:x=2 Let the centre of the circle be (h,0) and radius be ' r ' ⇒|h+2|2=|h−2|l=r⇒h2+4+4h=2h2+4−4h⇒h2−12h+4=0h=12±822=6±42⇒|h−2|=4(2−1),4(2+1)