A circle passes through the point (3,(7/2)^0.5) and touches the line pair x^2 – y^2 -2x+1=0. the co ordinates of centre of circle are?

1. (4,0)
   1. (6,0)

OK
so first we solve for the lines

whihc gives the two lines as

and now plotting them on the coordinate axes, it’s easy to see by symmetry that the center of circle would lie on x- axis and hence will be of the form
(a,0).
thus we can equate the radius
perpendicular distance from (a,0) to the line x+y=1 is equal to the distance between points

thus the equation will be

solving the quadratic we get a as
a=4 and a=6
so the answer is A and C