Give All Solutions of the Nonlinear System of Equations, Including $$\begin{array} { r } x y = 11 \\2 y ^ { 2 } - x ^ { 2 } = 11\end{array}$$

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
- $$\begin{array} { r } x y = 11 \\2 y ^ { 2 } - x ^ { 2 } = 11\end{array}$$

A) $\left\{ \left( - 22 , - \frac { 1 } { 2 } \right) , ( 11,1 ) \right\}$

B) $\left\{ \left( i \sqrt { 22 } , - \frac { i \sqrt { 22 } } { 2 } \right) , \left( - i \sqrt { 22 } , \frac { i \sqrt { 22 } } { 2 } \right) , ( \sqrt { 11 } , \sqrt { 11 } ) , ( - \sqrt { 11 } , - \sqrt { 11 } ) \right\}$

C) $\left\{ \left\{ \mathrm { i } \sqrt { 22 } , - \frac { \mathrm { i } \sqrt { 22 } } { 2 } \right\} , ( \sqrt { 11 } , \sqrt { 11 } ) \right\}$

D) $\{ ( 2 \mathrm { i } \sqrt { 11 } , - \mathrm { i } \sqrt { 11 } ) , ( - 2 \mathrm { i } \sqrt { 11 } , \mathrm { i } \sqrt { 11 } ) , ( \sqrt { 11 } , \sqrt { 11 } ) , ( - \sqrt { 11 } , - \sqrt { 11 } ) \}$