KEAM 2014 Math Paper

The centre and radius of given circle
x2+y2−2x−4y−20=0
is C1(1,2) and r=√12+22+20=5
since, the radii of the two circles are equal. therefore the two circles will touch externally and the point of contact will be the mid-point between two centres.
Let coordinate of the centre of required circle be(h,k)
∴‌‌‌

h+1

2

=5 and ‌

k+2

2

=5
⇒‌‌h=9 and k=8
Hence, the centre is (9,8)