It is given that, sα≡x2+y2+2αx+k=0 And sβ≡x2+y2+2βy−k=0 Now sα=0 is a point circle of, α2−k=0 α=±√k Thus, the centre of sα=(±√k,0) sβ=0 is point circle of β2+k=0 which does not exist. The option matching the first two answer is 3 Hence, the correct option is option 3