A hyperbola having the transverse axis of length, $\sqrt { 2 }$ has the same foci as that of the ellipse, $3 x ^ { 2 } + 4 y ^ { 2 } = 12$ then this hyperbola does not pass through which of the following points?
(1) $\left( \frac { 1 } { \sqrt { 2 } } , 0 \right)$\\
(2) $\left( - \sqrt { \frac { 3 } { 2 } } , 1 \right)$\\
(3) $\left( 1 , - \frac { 1 } { \sqrt { 2 } } \right)$\\
(4) $\left( \sqrt { \frac { 3 } { 2 } } , \frac { 1 } { \sqrt { 2 } } \right)$