If a variable line drawn through the intersection of the lines $\frac{x}{3}+\frac{y}{4}=1$ and $\frac{x}{4}+\frac{y}{3}=1$ , meets the coordinate axes at $\mathrm{A}$ and $\mathrm{B}$, $\left(A \ne B\right),$then the locus of the midpoint of $\mathrm{AB}$ is:

• Correct answer
  A

  $7xy=6\left(x+y\right)$
• B

  $4{\left(x+y\right)}^2-28\left(x+y\right)+49=0$
• C

  $6xy=7\left(x+y\right)$
• D

  $14{\left(x+y\right)}^2-97\left(x+y\right)+168=0$

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