AIEEE 2002 Math Solved Paper

Let the required circle be
x2+y2+2gx+2fy+c=0
Since it passes through (0,0) and (1,0)
⇒c=0 and g=−‌

1

2

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=‌

3

2

⇒f2=‌

9

4

−‌

1

4

=2
∴f=±√2
Hence, the centers of required circle are
(‌

1

2

⋅√2) or (‌

1

2

,−√2)