A circle C passing through the point $(1,1)$ bisects the circumference of the circle $x^2+y^2-2 x=0$. If C is orthogonal to the circle $x^2+y^2+2 y-3=0$ then the centre of the circle C is

• A

  $\left(-\frac{1}{2}, 0\right)$
• Correct answer
  B

  $\left(\frac{5}{2}, 0\right)$
• C

  $\left(0, \frac{5}{2}\right)$
• D

  $\left(0,-\frac{1}{2}\right)$

Hence, the correct answer is option: 'B'.