An object moves along an ellipse with equation

$4x^2+16x+16y^2-48=0($shown below$)$

Which of the following will determine the length of the path traveled by the object?

${\displaystyle \underset{-6}{\overset{2}{}}}\sqrt[\phantom{2}]{1+\frac{(8x+16{)}^2}{64(-4x^2-16x+48)}}$

${\displaystyle \underset{-6}{\overset{2}{}}}\sqrt[\phantom{2}]{\frac{-4x^2-16x+48}{16}}dx$

${\displaystyle \underset{-6}{\overset{2}{}}}\sqrt[\phantom{2}]{1+(8x+16+32y{)}^2}$