Give All Solutions of the Nonlinear System of Equations, Including $$x y = 11$$

Multiple Choice

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

A) $\left\{ \left( \mathrm { i } \sqrt { 22 } , - \frac { \mathrm { i } \sqrt { 22 } } { 2 } \right) , ( \sqrt { 11 } , \sqrt { 11 } ) \right\}$
B) $\left\{ \left( - 22 , - \frac { 1 } { 2 } \right) , ( 11,1 ) \right\}$
C) $\{ ( 2 \mathrm { i } \sqrt { 11 } , - \mathrm { i } \sqrt { 11 } ) , ( - 2 \mathrm { i } \sqrt { 11 } , \mathrm { i } \sqrt { 11 } ) , ( \sqrt { 11 } , \sqrt { 11 } ) , ( - \sqrt { 11 } , - \sqrt { 11 } ) \}$
D) $\left\{ \left( \mathrm { i } \sqrt { 22 } , - \frac { \mathrm { i } \sqrt { 22 } } { 2 } \right) , \left( - \mathrm { i } \sqrt { 22 } , \frac { \mathrm { i } \sqrt { 22 } } { 2 } \right) , ( \sqrt { 11 } , \sqrt { 11 } ) , ( - \sqrt { 11 } , - \sqrt { 11 } ) \right\}$