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 coordinates axes at A and B, $(A\ne B)$, then the locus of the midpoint of AB is

• A

  $6xy=7\left(x+y\right)$

• B

  $7xy=6\left(x+y\right)$

• C

  $4{(x+y)}^2-28(x+y)+49=0$

• D

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