If a tangent to the circle $x^2+y^2+2 x+2 y+1=0$ is radical axis of the circles $x^2+y^2+2 g x+2 f y+c=0$ and $2 x^2+2 y^2+3 x+8 y+2 c=0$, then

• A

  $g=\frac{3}{7}$ or $f=4$
• B

  $g=\frac{3}{2}$ or $f=\frac{2}{3}$
• C

  $g=\frac{3}{5}$ or $f=1$
• Correct answer
  D

  $g=\frac{3}{4}$ or $f=2$

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