The slope of the tangent to a curve $C : y = y(x)$ at any point $(x,y)$ on it is $\frac { 2e ^ { 2x } - 6e ^ { -x } + 9 } { 2 + 9e ^ { -2x } }$. If $C$ passes through the points $\left(0, \frac{1}{2} + \frac{\pi}{2\sqrt{2}}\right)$ and $\left(\alpha, \frac{1}{2} e ^ { 2\alpha }\right)$ then $e ^ { \alpha }$ is equal to\\
(1) $\frac { 3 + \sqrt { 2 } } { 3 - \sqrt { 2 } }$\\
(2) $\frac { 3 } { \sqrt { 2 } } \cdot \frac { 3 + \sqrt { 2 } } { 3 - \sqrt { 2 } }$\\
(3) $\frac { 1 } { \sqrt { 2 } } \cdot \frac { \sqrt { 2 } + 1 } { \sqrt { 2 } - 1 }$\\
(4) $\frac { \sqrt { 2 } + 1 } { \sqrt { 2 } - 1 }$