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