Let the required circle be
x2+y2+2gx+2fy+c=0 Since it passes through (0,0) and (1,0) On putting these values, we get
⇒c=0 and
g=− Points (0,0) and (1,0) lie inside the circle
x2+y2=9, so two circles touch internally
⇒c1c2=r1−r2 ∴√g2+f2=3−√g2+f2⇒√g2+f2= Squaring both side, we get
⇒f2=−=2∴f=±√2 Hence, the centres of required circle are
(,√2) or
(,−√2)