The centre of a circle passing through the points (0,0) , (1,0)  and touching the circle x2+y2=9  is

Circle passes through (0,0)  and (1,0) , so let the equation of the circle be x2+y2−x+ky=0  solving with x2+y2=9 We get 9−x+ky=0 ⇒    x=9+ky ⇒    (9+ky)2+y2=9 ⇒    (k2+1)y2+18ky+72=0 For equal roots (18k)2−4.72(k2+1)=0 ⇒  k=±22 Hence the coordinates of the centre are (12,2)  or (12,−2)