Solve the Problem $( - 4,1 )$ Whose Length Integral $1 \leq y \leq 2$

Multiple Choice

Solve the problem.
-Find a curve through the point $( - 4,1 )$ whose length integral, $1 \leq y \leq 2$ , is $L = \int _ { 1 } ^ { 2 } \sqrt { 1 + \frac { 4 } { y ^ { 3 } } } \mathrm { dy }$ .

A) $x = \frac { 2 } { \sqrt { y } }$
B) $x = \frac { - 4 } { \sqrt { y } }$
C) $x = - 4 y ^ { 5 / 2 }$
D) $x = - 4 \sqrt { y }$