Let $\alpha, \beta$ be the roots of $x^2+5 x+6=0$ and $\gamma, \delta$ be the roots of $y^2+6 y+7=0$. Then the equation of the circle with $(\alpha, \gamma)$ and $(\beta, \delta)$ as the extremities of a diameter is

• A

  $x^2+y^2+5 x+6 y+10=0$
• B

  $x^2+y^2+5 x+6 y+11=0$
• Correct answer
  C

  $x^2+y^2+5 x+6 y+13=0$
• D

  $x^2+y^2+5 x+6 y+12=0$

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