Determine the Real Solutions to the System of Nonlinear Equations $$\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 27 \\x ^ { 2 } + y ^ { 2 } = 51\end{array}$$

Multiple Choice

Determine the real solutions to the system of nonlinear equations.
- $$\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 27 \\x ^ { 2 } + y ^ { 2 } = 51\end{array}$$

A) $( 0,0 )$
B) $( \sqrt { 39 } , 2 \sqrt { 3 } ) , ( - \sqrt { 39 } , 2 \sqrt { 3 } )$
C) $( \sqrt { 39 } , 2 \sqrt { 3 } ) , ( - \sqrt { 39 } , 2 \sqrt { 3 } ) , ( \sqrt { 39 } , - 2 \sqrt { 3 } ) , ( - \sqrt { 39 } , - 2 \sqrt { 3 } )$
D) $( \sqrt { 39 } , 2 \sqrt { 3 } ) , ( - \sqrt { 39 } , - 2 \sqrt { 3 } )$