Let the equation of the circle is x2+y2+2gx+2fy+c=0 at (0,0),0+0+0+0+c=0⇒c=0 at ‌‌(2,0),4+0+2g⋅2+0+0=0 ⇒‌‌g=−1 at (0,−2),0+4+0−4f+0=0⇒f=1 at (k,−2),k2+4+2kg−4f+0=0 ⇒‌‌k2+4−2k−4=0 ⇒‌‌k(k−2)=0 ⇒‌‌k=0,k=2