Manipal Entrance Test 2016 Math Paper

Let the equation of circle be x2+y2+2gx+2fy+c=0
since, it passes through the point (2a,0), so
4a2+4ag+c=0 ...(i)
Also, its radical axis with x2+y2=a2 is
2ax+2fy+c+a2=0
But the radical axis is x=

a

2

, so we get
or

2g

1

=

c+a

−a∕2

and f=0
or ag+c+a=0 ...(ii)
From Eqs. (i) and (ii), we get g and c
Hence, the equation is x2+y2−2ax=0