Let $\mathbf { k }$ be a nonzero real number such that
$$\begin{aligned}
& x ^ { 2 } + y ^ { 2 } = ( 6 k ) ^ { 2 } \\
& ( x - 2 k ) ^ { 2 } + y ^ { 2 } = ( 2 k \sqrt { 5 } ) ^ { 2 }
\end{aligned}$$
Accordingly, which of the following is the equivalent of $x ^ { 2 } - y ^ { 2 }$ in terms of $k$?\\
A) $13 \mathrm { k } ^ { 2 }$\\
B) $14 \mathrm { k } ^ { 2 }$\\
C) $15 k ^ { 2 }$