The correct option is
C x2+y2−18x+9=0Given that
x=1 is radical axis of two circles. Therefore the line joining centers should be perpendicular to
x=1Since the center of one circle is (0,0) , the center of another circle should lie on y=0
Let the center of another circle be (a,0) and the radius be r
The equation of circle is (x−a)2+y2=r2
Given that the two circles are orthogonal,
We get a2=r2+9
here the centers of two circles are (0,0) and (a,0), radius of two circles are 3 and r respectively.
Since the length of tangents from radical axis are equal, we get (1−a)2+0−r2=1−9
⇒a2−r2=2a−9
We know that a2−r2=9 from orthogonal condition
By solving both equations, we get a=9 and r2=72
Therefore the equation of required circle will be x2+y2−18x+9=0
So the correct option is C