The centre of the circle touching the circles $x^2+y^2-4 x-6 y-12=0$, $x^2+y^2+6 x+18 y+26=0$ at their point of contact and passing through the point $(1,-1)$ is

• Correct answer
  A

  $\left(\frac{1}{3},-1\right)$
• B

  $\left(\frac{1}{5}, \frac{6}{5}\right)$
• C

  $\left(\frac{1}{2}, 1\right)$
• D

  $\left(-\frac{1}{4},-\frac{1}{2}\right)$

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