Solve the Nonlinear System of Equations $$\left\{ \begin{array} { l } x ^ { 2 } + 2 y ^ { 2 } = 8 \\x ^ { 2 } - 2 y ^ { 2 } = 12\end{array} \right.$$

Multiple Choice

Solve the nonlinear system of equations.
- $$\left\{ \begin{array} { l } x ^ { 2 } + 2 y ^ { 2 } = 8 \\x ^ { 2 } - 2 y ^ { 2 } = 12\end{array} \right.$$

A) $( \sqrt { 10 } , \sqrt { 2 } ) , ( \sqrt { 10 } , - \sqrt { 2 } )$
B) $( \sqrt { 10 } , \sqrt { 2 } ) , ( \sqrt { 10 } , - \sqrt { 2 } ) , ( - \sqrt { 10 } , \sqrt { 2 } ) , ( - \sqrt { 10 } , - \sqrt { 2 } )$
C) $( \sqrt { 10 } , \sqrt { 2 } ) , ( - \sqrt { 10 } , - \sqrt { 2 } )$
D) $\varnothing$