Equation of Family of Circles Touching a Line and Passing through a Given Point on the Line

Q.

A circle passes through the point $(3,\sqrt{\frac{7}{2}})$ and touches the line pair $x^2-y^2-2x+1=0$. The coordinates of the centre of the circle are

1. (0, 4)

2. (5, 0)

3. (6, 0)

4. none of these