If $4 x^2+12 x y+9 y^2+2 \mathrm{~g} x+2 \mathrm{f} y-1=0$ represent a pair of parallel lines then

• A

  $\frac{f}{g}+\frac{g}{f}+\frac{13}{6}=0$
• B

  $\mathrm{f}^2+\mathrm{g}^2=\mathrm{fg}$
• C

  $\mathrm{f}^2+\mathrm{g}^2=6 \mathrm{fg}$
• Correct answer
  D

  $\frac{f}{g}+\frac{g}{f}=\frac{13}{6}$

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